377 results
Search Results
2. Adaptive Multi-Innovation Gradient Identification Algorithms for a Controlled Autoregressive Autoregressive Moving Average Model.
- Author
-
Xu, Ling, Xu, Huan, and Ding, Feng
- Subjects
- *
MOVING average process , *COST functions , *STOCHASTIC convergence , *DYNAMICAL systems , *ALGORITHMS , *IDENTIFICATION , *TECHNOLOGY convergence - Abstract
The controlled autoregressive autoregressive moving average (CARARMA) models are of popularity to describe the evolution characteristics of dynamical systems. To overcome the identification obstacle resulting from colored noises, this paper studies the identification of the CARARMA models by forming an intermediate correlated noise model. In order to realize the real-time prediction function of the models, the on-line identification scheme is developed by constructing the dynamical objective functions based on the real-time sampled observations. Firstly, a rolling optimization cost function is built based on the observation at a single sampling instant to catch the modal information at a single time point and a generalized extended stochastic gradient (GESG) algorithm is proposed through the stochastic gradient optimization. Secondly, a rolling window cost function is built in accordance with the dynamical batch observations within data window by extending the proposed GESG algorithm and the multi-innovation generalized extended stochastic gradient algorithm is derived. Thirdly, from the perspective of theoretical analysis, the convergence proof of the proposed algorithm is provided based on the stochastic martingale convergence theory. Finally, the simulation analysis and comparison studies are provided to show the performance of the proposed algorithms. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
3. Low-Complexity $$l_0$$ -Norm Penalized Shrinkage Linear and Widely Linear Affine Projection Algorithms.
- Author
-
Zhang, Youwen, Xiao, Shuang, Sun, Dajun, and Liu, Lu
- Subjects
COMPUTATIONAL complexity ,COST functions ,ALGORITHMS ,TIME-varying systems ,STOCHASTIC convergence - Abstract
In this paper, we propose an $$l_0$$ -norm penalized shrinkage linear affine projection ( $$l_0$$ -SL-AP) algorithm and an $$l_0$$ -norm penalized shrinkage widely linear affine projection ( $$l_0$$ -SWL-AP) algorithm. The proposed algorithms provide variable step-size by minimizing the noise-free a posteriori error at each iteration and introduce an $$l_0$$ -norm constraint to the cost function. The $$l_0$$ -SWL-AP algorithm also exploits noncircular properties of the input signal. In contrast with conventional AP algorithms, the proposed algorithms increase the estimation accuracy for time-varying sparse system identification. A quantitative analysis of the convergence behavior for the $$l_0$$ -SWL-AP algorithm verifies the capabilities of the proposed algorithms. To reduce the complexity, we also introduce dichotomous coordinate descent (DCD) iterations to the proposed algorithms ( $$l_0$$ -SL-DCD-AP and $$l_0$$ -SWL-DCD-AP) in this paper. Simulations indicate that the $$l_0$$ -SL-AP and $$l_0$$ -SWL-AP algorithms provide faster convergence speed and lower steady-state misalignment than the previous APA-type algorithms. The $$l_0$$ -SL-DCD-AP and $$l_0$$ -SWL-DCD-AP algorithms perform similarly to their counterparts but with reduced complexity. [ABSTRACT FROM AUTHOR]
- Published
- 2017
- Full Text
- View/download PDF
4. A convergence analysis for a convex version of Dikin's algorithm.
- Author
-
Jie Sun
- Subjects
STOCHASTIC convergence ,ALGORITHMS ,CONVEX programming ,LINEAR programming ,MATHEMATICAL programming - Abstract
This paper is concerned with the convergence property of Dikin's algorithm applied to linearly constrained smooth convex programs. We study a version of Dikin's algorithm in which a second-order approximation of the objective function is minimized at each iteration together with an affine transformation of the variables. We prove that the sequence generated by the algorithm globally converges to a limit point at a local linear rate if the objective function satisfies a Hessian similarity condition. The result is of a theoretical nature in the sense that in order to ensure that the limit point is an ε-optimal solution, one may have to restrict the steplength to the order of O(ε). The analysis does not depend on non-degeneracy assumptions. [ABSTRACT FROM AUTHOR]
- Published
- 1996
- Full Text
- View/download PDF
5. Multidimensional Blind Separation Using Higher-Order Statistics: Application to Non-Cooperative STBC Systems.
- Author
-
Luo, Minggang, Li, Liping, Qian, Guobing, and Liao, Hongshu
- Subjects
SPACE-time block codes ,INDEPENDENT component analysis ,ALGORITHMS ,STOCHASTIC convergence ,COMPUTER simulation - Abstract
Blindly separating the intercepted signals is a challenging problem in non-cooperative multiple input multiple output systems in association with space-time block code (STBC) where channel state information and coding matrix are unavailable. To our knowledge, there is no report on dealing with this problem in literature. In this paper, the STBC systems are represented with an independent component analysis (ICA) model by merging the channel and coding matrices as virtual channel matrix. Analysis shows that the source signals are of group-wise independence and the condition of mutual independence can not be satisfied for ordinary ICA algorithms when specific modulations are employed. A new multidimensional ICA algorithm is proposed to separate the intercepted signals in this case by jointly block-diagonalizing (JBD) the cumulant matrices. In this paper, JBD is achieved by a 2-step optimization algorithm and a contrast function is derived from the JBD criterion to remove the additional permutation ambiguity with explicit mathematical explanations. The convergence of the new method is guaranteed. Compared with the ICA-based channel estimation methods, simulations show that the new algorithm, which does not introduce additional ambiguities, achieves better performance with faster convergence in a non-cooperative scenario. [ABSTRACT FROM AUTHOR]
- Published
- 2014
- Full Text
- View/download PDF
6. Normalized Subband Adaptive Filter Algorithm with Combined Step Size for Acoustic Echo Cancellation.
- Author
-
Shen, Zijie, Yu, Yi, and Huang, Tianmin
- Subjects
ADAPTIVE filters ,ELECTRIC filters ,STOCHASTIC convergence ,ELECTRIC networks ,SIGNAL filtering ,ALGORITHMS - Abstract
A novel normalized subband adaptive filter algorithm with combined step size is proposed for acoustic echo cancellation, which is derived by utilizing a variable mixing parameter to combine a large step size and a small one, thus providing fast convergence rate and small steady-state error. The mixing parameter is indirectly updated by utilizing the stochastic gradient method which minimizes the sum of squared subband errors. Simulation results demonstrate the superiority of the proposed algorithm in terms of the convergence rate and steady-state error as compared to other algorithms mentioned in this paper. [ABSTRACT FROM AUTHOR]
- Published
- 2017
- Full Text
- View/download PDF
7. A simplified global convergence proof of the affine scaling algorithm.
- Author
-
Monteiro, R. D. C., Tsuchiya, T., and Wang, Y.
- Subjects
AFFINE geometry ,LINEAR programming ,STOCHASTIC convergence ,ALGORITHMS ,FRACTIONS ,OPERATIONS research - Abstract
This paper presents a simplified and self-contained global convergence proof for the affine scaling algorithm applied to degenerate linear programming problems. Convergence of the sequence of dual estimates to the center of the optimal dual face is also proven. In addition, we give a sharp rate of convergence result for the sequence of objective function values. All these results are proved with respect to the long step version of the affine scaling algorithm in which we move a fraction λ, where λ ϵ (0,2/3], of the step to the boundary of the feasible region. [ABSTRACT FROM AUTHOR]
- Published
- 1993
- Full Text
- View/download PDF
8. ADMM for monotone operators: convergence analysis and rates.
- Author
-
Boţ, Radu Ioan and Csetnek, Ernö Robert
- Subjects
MONOTONE operators ,STOCHASTIC convergence ,ALGORITHMS - Abstract
We propose in this paper a unifying scheme for several algorithms from the literature dedicated to the solving of monotone inclusion problems involving compositions with linear continuous operators in infinite dimensional Hilbert spaces. We show that a number of primal-dual algorithms for monotone inclusions and also the classical ADMM numerical scheme for convex optimization problems, along with some of its variants, can be embedded in this unifying scheme. While in the first part of the paper, convergence results for the iterates are reported, the second part is devoted to the derivation of convergence rates obtained by combining variable metric techniques with strategies based on suitable choice of dynamical step sizes. The numerical performances, which can be obtained for different dynamical step size strategies, are compared in the context of solving an image denoising problem. [ABSTRACT FROM AUTHOR]
- Published
- 2019
- Full Text
- View/download PDF
9. Limited range spatial load balancing in non-convex environments using sampling-based motion planners.
- Author
-
Boardman, Beth, Harden, Troy, and Martínez, Sonia
- Subjects
MECHANICAL loads ,ROAD maps ,PROBABILISTIC inference ,STOCHASTIC convergence ,ALGORITHMS - Abstract
This paper analyzes the limited range, spatial load balancing problem for agents deployed in non-convex environments and subject to differential constraints which restricts how the agents can move. First, the (unlimited range) spatial load balancing problem is introduced and the minimization problem with area constraints is defined. Then, to extend the problem for limited ranges, two cost functions and a sub-partition are defined. The problems are then analyzed and the results prove the existence of a partition that satisfies the area constraints. The non-convex environment makes the problem difficult to solve in continuous-space. Therefore, a probabilistic roadmap is used to approximate agents’ cells via a graph. A distributed algorithm is proven to converge to an approximate solution. Finally, the convergence of the algorithm is shown in simulation. [ABSTRACT FROM AUTHOR]
- Published
- 2018
- Full Text
- View/download PDF
10. Robust Evolutionary Algorithm Design for Socio-economic Simulation.
- Author
-
Alkemade, Floortje, Poutré, Han La, and Amman, Hans M.
- Subjects
COMPUTER science ,EVOLUTIONARY economics ,EVOLUTIONARY computation ,SOCIAL learning ,ALGORITHMS ,SIMULATION methods & models ,ECONOMIC models ,STOCHASTIC convergence - Abstract
Agent-based computational economics (ACE) combines elements from economics and computer science. In this paper, we focus on the relation between the evolutionary technique that is used and the economic problem that is modeled. In the field of ACE, economic simulations often derive parameter settings for the evolutionary algorithm directly from the values of the economic model parameters. In this paper, we compare two important approaches that are dominating ACE research and show that the above practice may hinder the performance of the evolutionary algorithm and thereby hinder agent learning. More specifically, we show that economic model parameters and evolutionary algorithm parameters should be treated separately by comparing the two widely used approaches to social learning with respect to their convergence properties and robustness. This leads to new considerations for the methodological aspects of evolutionary algorithm design within the field of ACE. [ABSTRACT FROM AUTHOR]
- Published
- 2006
- Full Text
- View/download PDF
11. The robust constant and its applications in random global search for unconstrained global optimization.
- Author
-
Peng, Zheng, Wu, Donghua, and Zhu, Wenxing
- Subjects
ROBUST optimization ,GLOBAL optimization ,MATHEMATICAL optimization ,MATHEMATICAL analysis ,ALGORITHMS ,STOCHASTIC convergence - Abstract
Robust analysis is important for designing and analyzing algorithms for global optimization. In this paper, we introduce a new concept, robust constant, to quantitatively characterize the robustness of measurable sets and functions. The new concept is consistent to the theoretical robustness presented in literatures. This paper shows that, from the respects of convergence theory and numerical computational cost, robust constant is valuable significantly for analyzing random global search methods for unconstrained global optimization. [ABSTRACT FROM AUTHOR]
- Published
- 2016
- Full Text
- View/download PDF
12. Iterative algorithm for a family of split equilibrium problems and fixed point problems in Hilbert spaces with applications.
- Author
-
Wang, Shenghua, Gong, Xiaoying, Abdou, Afrah, and Cho, Yeol
- Subjects
FIXED point theory ,ITERATIVE methods (Mathematics) ,ALGORITHMS ,HILBERT space ,STOCHASTIC convergence - Abstract
In this paper, we propose an iterative algorithm and, by using the proposed algorithm, prove some strong convergence theorems for finding a common element of the set of solutions of a finite family of split equilibrium problems and the set of common fixed points of a countable family of nonexpansive mappings in Hilbert spaces. An example is given to illustrate the main result of this paper. As an application, we construct an algorithm to solve an optimization problem. [ABSTRACT FROM AUTHOR]
- Published
- 2016
- Full Text
- View/download PDF
13. Split equality problem and multiple-sets split equality problem for quasi-nonexpansive multi-valued mappings.
- Author
-
Yujing Wu, Rudong Chen, and Luo Yi Shi
- Subjects
NONEXPANSIVE mappings ,STOCHASTIC convergence ,HILBERT space ,HAUSDORFF spaces ,METRIC spaces ,LINEAR operators ,ALGORITHMS ,NUMERICAL analysis - Abstract
The multiple-sets split equality problem (MSSEP) requires finding a point x ∈∩
N i=1 Ci , y ∈∩M j=1 Qj , such that Ax = By, where N and M are positive integers, {C1 , C2 ,..., CN } and {Q1 ,Q2 ,...,QM } are closed convex subsets of Hilbert spaces H1 , H2 , respectively, and A : H1 →H3 , B : H2 →H3 are two bounded linear operators. When N = M = 1, the MSSEP is called the split equality problem (SEP). If let B = I, then the MSSEP and SEP reduce to the well-known multiple-sets split feasibility problem (MSSFP) and split feasibility problem (SFP), respectively. Recently, some authors proposed many algorithms to solve the SEP and MSSEP. However, to implement these algorithms, one has to find the projection on the closed convex sets, which is not possible except in simple cases. One of the purposes of this paper is to study the SEP and MSSEP for a family of quasi-nonexpansive multi-valued mappings in the framework of infinite-dimensional Hilbert spaces, and propose an algorithm to solve the SEP and MSSEP without the need to compute the projection on the closed convex sets. [ABSTRACT FROM AUTHOR]- Published
- 2014
- Full Text
- View/download PDF
14. A modified nonmonotone BFGS algorithm for unconstrained optimization.
- Author
-
Li, Xiangrong, Wang, Bopeng, and Hu, Wujie
- Subjects
CONSTRAINED optimization ,ALGORITHMS ,STOCHASTIC convergence ,LINEAR systems ,CONVEX functions ,MONOTONE operators - Abstract
In this paper, a modified BFGS algorithm is proposed for unconstrained optimization. The proposed algorithm has the following properties: (i) a nonmonotone line search technique is used to obtain the step size $\alpha_{k}$ to improve the effectiveness of the algorithm; (ii) the algorithm possesses not only global convergence but also superlinear convergence for generally convex functions; (iii) the algorithm produces better numerical results than those of the normal BFGS method. [ABSTRACT FROM AUTHOR]
- Published
- 2017
- Full Text
- View/download PDF
15. Strong convergence theorems by hybrid and shrinking projection methods for sums of two monotone operators.
- Author
-
Yuying, Tadchai and Plubtieng, Somyot
- Subjects
STOCHASTIC convergence ,MATHEMATICS theorems ,MONOTONE operators ,ALGORITHMS ,GRAPHICAL projection - Abstract
In this paper, we introduce two iterative algorithms for finding the solution of the sum of two monotone operators by using hybrid projection methods and shrinking projection methods. Under some suitable conditions, we prove strong convergence theorems of such sequences to the solution of the sum of an inverse-strongly monotone and a maximal monotone operator. Finally, we present a numerical result of our algorithm which is defined by the hybrid method. [ABSTRACT FROM AUTHOR]
- Published
- 2017
- Full Text
- View/download PDF
16. Strong convergence of an extragradient-type algorithm for the multiple-sets split equality problem.
- Author
-
Zhao, Ying and Shi, Luoyi
- Subjects
STOCHASTIC convergence ,ALGORITHMS ,HILBERT space ,EQUALITY ,COEFFICIENTS (Statistics) - Abstract
This paper introduces a new extragradient-type method to solve the multiple-sets split equality problem (MSSEP). Under some suitable conditions, the strong convergence of an algorithm can be verified in the infinite-dimensional Hilbert spaces. Moreover, several numerical results are given to show the effectiveness of our algorithm. [ABSTRACT FROM AUTHOR]
- Published
- 2017
- Full Text
- View/download PDF
17. Convergence results of a matrix splitting algorithm for solving weakly nonlinear complementarity problems.
- Author
-
Luo, Mei-Ju, Wang, Ya-Yi, and Liu, Hong-Ling
- Subjects
STOCHASTIC convergence ,MATRICES (Mathematics) ,ALGORITHMS ,LINEAR complementarity problem ,NONLINEAR theories - Abstract
In this paper, we consider a class of weakly nonlinear complementarity problems (WNCP) with large sparse matrix. We present an accelerated modulus-based matrix splitting algorithm by reformulating the WNCP as implicit fixed point equations based on two splittings of the system matrixes. We show that, if the system matrix is a P-matrix, then under some mild conditions the sequence generated by the algorithm is convergent to the solution of WNCP. [ABSTRACT FROM AUTHOR]
- Published
- 2016
- Full Text
- View/download PDF
18. A novel parameter estimation method for metal oxide surge arrester models.
- Author
-
NAFAR, MEHDI, GHAREHPETIAN, GEVORK, and NIKNAM, TAHER
- Subjects
PARAMETER estimation ,METALLIC oxides ,MATHEMATICAL models ,PARTICLE swarm optimization ,ALGORITHMS ,PHYSICS experiments ,STOCHASTIC convergence - Abstract
Accurate modelling and exact determination of Metal Oxide (MO) surge arrester parameters are very important for arrester allocation, insulation coordination studies and systems reliability calculations. In this paper, a new technique, which is the combination of Adaptive Particle Swarm Optimization (APSO) and Ant Colony Optimization (ACO) algorithms and linking the MATLAB and EMTP, is proposed to estimate the parameters of MO surge arrester models. The proposed algorithm is named Modified Adaptive Particle Swarm Optimization (MAPSO). In the proposed algorithm, to overcome the drawback of the PSO algorithm (convergence to local optima), the inertia weight is tuned by using fuzzy rules and the cognitive and the social parameters are self-adaptively adjusted. Also, to improve the global search capability and prevent the convergence to local minima, ACO algorithm is combined to the proposed APSO algorithm. The transient models of MO surge arrester have been simulated by using ATP-EMTP. The results of simulations have been applied to the program, which is based on MAPSO algorithm and can determine the fitness and parameters of different models. The validity and the accuracy of estimated parameters of surge arrester models are assessed by comparing the predicted residual voltage with experimental results. [ABSTRACT FROM AUTHOR]
- Published
- 2011
- Full Text
- View/download PDF
19. On the Convergence of a Parallel Iterative Algorithm for Two Finite Families of Uniformly L-Lipschitzian Mappings.
- Author
-
FENG GU
- Subjects
STOCHASTIC convergence ,ITERATIVE methods (Mathematics) ,MATHEMATICAL mappings ,BANACH spaces ,ALGORITHMS ,CONVEX sets - Abstract
In this paper, we study a necessary and sufficient condition for the strong convergence of a parallel iterative algorithm for two finite families of uniformly L-Lipschitzian mappings in Banach spaces. The results presented in this paper improve and extend the recent ones announced by S. S. Chang, Y. J. Cho, E. U. Ofoedu, J. Schu, L. C. Zeng and many others. [ABSTRACT FROM AUTHOR]
- Published
- 2011
20. Injection moulding optimisation of multi-class design variables using a PSO algorithm.
- Author
-
Deng, Y.-M., Zheng, D., and Lu, X.-J.
- Subjects
MOLDING (Founding) ,ALGORITHMS ,MATHEMATICAL optimization ,STOCHASTIC convergence ,COMPUTER software - Abstract
Injection moulding optimisation seeks to achieve the highest possible moulding quality under the specified constraints. To this end, the factors (design variables) affecting the moulding quality should be adjusted, including those of process parameters, mould design, part geometry, etc. Past work in this aspect is primarily focused on tuning the process parameters and mould design (e.g., gate location, runner and cooling channel layout), with less attention on the part geometry, and none on them all. To address this problem, this paper presents a PSO (particle swarm optimisation) algorithm for the optimisation of multi-class design variables, such as the part thickness, process parameters (melt temperature, mould temperature, injection time) and gate location. The optimisation is targeted at different aspects of moulding quality, including part warpage, weld lines, air traps, and so on. In applying the PSO algorithm, the paper proposes a modified elite archiving method, which can expedite the convergence speed, hence improving the efficiency of the algorithm. A computer program was developed that automates the steps such as adjusting the part thickness, the injection moulding process parameters and the gate location, activating the CAE software to simulate the injection moulding process, retrieving the simulation results, and evaluating the objective functions. The whole procedure iterates a number of generations by following the search process of the algorithm. A case study was also presented to illustrate as well as to test the proposed methodology, which was demonstrated as both effective and efficient. [ABSTRACT FROM AUTHOR]
- Published
- 2008
- Full Text
- View/download PDF
21. A trust region spectral method for large-scale systems of nonlinear equations.
- Author
-
Zeng, Meilan and Zhou, Guanghui
- Subjects
NONLINEAR equations ,STOCHASTIC convergence ,ALGORITHMS ,JACOBIAN matrices ,QUASI-Newton methods - Abstract
The spectral gradient method is one of the most effective methods for solving large-scale systems of nonlinear equations. In this paper, we propose a new trust region spectral method without gradient. The trust region technique is a globalization strategy in our method. The global convergence of the proposed algorithm is proved. The numerical results show that our new method is more competitive than the spectral method of La Cruz et al. (Math. Comput. 75(255):1429-1448, ) for large-scale nonlinear equations. [ABSTRACT FROM AUTHOR]
- Published
- 2016
- Full Text
- View/download PDF
22. Convergence theorems for split equality mixed equilibrium problems with applications.
- Author
-
Ma, Zhaoli, Wang, Lin, Chang, Shih-sen, and Duan, Wen
- Subjects
STOCHASTIC convergence ,EQUILIBRIUM ,ALGORITHMS ,INFINITY (Mathematics) ,HILBERT space ,VARIATIONAL inequalities (Mathematics) - Abstract
In this paper, we introduce a new algorithm for solving split equality mixed equilibrium problems in the framework of infinite-dimensional real Hilbert spaces. The strong and weak convergence theorems are obtained. As application, we shall utilize our results to study the split equality mixed variational inequality problem and the split equality convex minimization problem. Our results presented in this paper improve and extend some recent corresponding results. [ABSTRACT FROM AUTHOR]
- Published
- 2015
- Full Text
- View/download PDF
23. Some sharp continued fraction inequalities for the Euler-Mascheroni constant.
- Author
-
You, Xu and Chen, Di-Rong
- Subjects
EULER number ,STOCHASTIC convergence ,CONTINUED fractions ,MATHEMATICAL inequalities ,RATIONAL numbers ,ALGORITHMS - Abstract
The aim of this paper is to establish some new continued fraction inequalities for the Euler-Mascheroni constant by multiple-correction method. [ABSTRACT FROM AUTHOR]
- Published
- 2015
- Full Text
- View/download PDF
24. Iterative process for solving a multiple-set split feasibility problem.
- Author
-
Dang, Yazheng and Xue, Zhonghui
- Subjects
FEASIBILITY problem (Mathematical optimization) ,SUBGRADIENT methods ,ALGORITHMS ,STOCHASTIC convergence ,CONVEX sets - Abstract
This paper deals with a variant relaxed CQ algorithm by using a new searching direction, which is not the gradient of a corresponding function. The strategy is to intend to improve the convergence. Its convergence is proved under some suitable conditions. Numerical results illustrate that our variant relaxed CQ algorithm converges more quickly than the existing algorithms. [ABSTRACT FROM AUTHOR]
- Published
- 2015
- Full Text
- View/download PDF
25. Degeneracy in interior point methods for linear programming: a survey.
- Author
-
0. Güler, den Hertog, D., Roos, C., Terlaky, T., and Tsuchiya, T.
- Subjects
LINEAR programming ,MATHEMATICAL programming ,STOCHASTIC convergence ,ALGORITHMS ,RESEARCH ,SURVEYS - Abstract
The publication of Karmarkar's paper has resulted in intense research activity into Interior Point Methods (IPMs) for linear programming. Degeneracy is present in most real-life problems and has always been an important issue in linear programming, especially in the Simplex method. Degeneracy is also an important issue in IPMs. However, the difficulties are different in the two methods. In this paper, we survey the various theoretical and practical issues related to degeneracy in IPMs for linear programming. We survey results, which, for the most part, have already appeared in the literature. Roughly speaking, we shall deal with the effect of degeneracy on the following: the convergence of IPMs, the trajectories followed by the algorithms, numerical performance, and finding basic solutions. [ABSTRACT FROM AUTHOR]
- Published
- 1993
26. A Ljusternik-Schnirelman minimax algorithm for finding equality constrained saddle points and its application for solving eigen problems: part I. Algorithm and global convergence.
- Author
-
Yao, Xudong
- Subjects
LJUSTERNIK-Schnirelman theory ,ALGORITHMS ,STOCHASTIC convergence - Abstract
In Yao (J. Sci. Comput. 66, 19-40 2016), two Ljusternik-Schnirelman minimax algorithms for capturing multiple free saddle points are developed from well-known Ljusternik-Schnirelman critical point theory, numerical experiment is carried out and global convergence is established. In this paper, a Ljusternik-Schnirelman minimax algorithm for calculating multiple equality constrained saddle points is presented. The algorithm is applied to numerically solve eigen problems. Finally, global convergence for the algorithm is verified. [ABSTRACT FROM AUTHOR]
- Published
- 2019
- Full Text
- View/download PDF
27. Optimization over the Pareto outcome set associated with a convex bi-objective optimization problem: theoretical results, deterministic algorithm and application to the stochastic case.
- Author
-
Bonnel, Henri and Collonge, Julien
- Subjects
PARETO optimum ,MATHEMATICAL optimization ,ALGORITHMS ,RANDOM functions (Mathematics) ,STOCHASTIC convergence - Abstract
Our paper consists of two main parts. In the first one, we deal with the deterministic problem of minimizing a real valued function $$f$$ over the Pareto outcome set associated with a deterministic convex bi-objective optimization problem (BOP), in the particular case where $$f$$ depends on the objectives of (BOP), i.e. we optimize over the Pareto set in the outcome space. In general, the optimal value $$U$$ of such a kind of problem cannot be computed directly, so we propose a deterministic outcome space algorithm whose principle is to give at every step a range (lower bound, upper bound) that contains $$U$$ . Then we show that for any given error bound, the algorithm terminates in a finite number of steps. In the second part of our paper, in order to handle also the stochastic case, we consider the situation where the two objectives of (BOP) are given by expectations of random functions, and we deal with the stochastic problem $$(S)$$ of minimizing a real valued function $$f$$ over the Pareto outcome set associated with this Stochastic bi-objective Optimization Problem (SBOP). Because of the presence of random functions, the Pareto set associated with this type of problem cannot be explicitly given, and thus it is not possible to compute the optimal value $$V$$ of problem $$(S)$$ . That is why we consider a sequence of Sample Average Approximation problems (SAA- $$N$$ , where $$N$$ is the sample size) whose optimal values converge almost surely to $$V$$ as the sample size $$N$$ goes to infinity. Assuming $$f$$ nondecreasing, we show that the convergence rate is exponential, and we propose a confidence interval for $$V$$ . Finally, some computational results are given to illustrate the paper. [ABSTRACT FROM AUTHOR]
- Published
- 2015
- Full Text
- View/download PDF
28. Strong convergence of a general iterative algorithm for a finite family of accretive operators in Banach spaces.
- Author
-
Song, Yanlai and Ceng, Luchuan
- Subjects
STOCHASTIC convergence ,ITERATIVE methods (Mathematics) ,ALGORITHMS ,OPERATOR theory ,BANACH spaces ,VARIATIONAL inequalities (Mathematics) - Abstract
The purpose of this paper is to present a new iterative scheme for finding a common solution to a variational inclusion problem with a finite family of accretive operators and a modified system of variational inequalities in infinite-dimensional Banach spaces. Under mild conditions, a strong convergence theorem for approximating this common solution is proved. The methods in the paper are novel and different from those in the early and recent literature. [ABSTRACT FROM AUTHOR]
- Published
- 2015
- Full Text
- View/download PDF
29. A scalable multisplitting algorithm to solve large sparse linear systems.
- Author
-
Couturier, Raphaël and Lilia, Ziane
- Subjects
ALGORITHMS ,LINEAR systems ,SPLITTING extrapolation method ,KRYLOV subspace ,ITERATIVE methods (Mathematics) ,STOCHASTIC convergence ,EXPERIMENTS - Abstract
In this paper, we revisit the Krylov multisplitting algorithm presented in Huang and O'Leary (Linear Algebra Appl 194:9-29, ) which uses a sequential method to minimize the Krylov iterations computed by a multisplitting algorithm. Our new algorithm is based on a parallel multisplitting algorithm with few blocks of large size using a parallel GMRES method inside each block and on a parallel Krylov minimization to improve the convergence. Some large-scale experiments with a 3D Poisson problem are presented with up to 8,192 cores. They show the obtained improvements compared to a classical GMRES both in terms of number of iterations and in terms of execution times. [ABSTRACT FROM AUTHOR]
- Published
- 2015
- Full Text
- View/download PDF
30. Iterative process for solving a multiple-set split feasibility problem.
- Author
-
Yazheng Dang and Zhonghui Xue
- Subjects
ITERATIVE methods (Mathematics) ,ALGORITHMS ,MATHEMATICAL functions ,STOCHASTIC convergence ,NUMERICAL calculations - Abstract
This paper deals with a variant relaxed CQ algorithm by using a new searching direction, which is not the gradient of a corresponding function. The strategy is to intend to improve the convergence. Its convergence is proved under some suitable conditions. Numerical results illustrate that our variant relaxed CQ algorithm converges more quickly than the existing algorithms. [ABSTRACT FROM AUTHOR]
- Published
- 2015
- Full Text
- View/download PDF
31. An algorithm with strong convergence for the split common fixed point problem of total asymptotically strict pseudocontraction mappings.
- Author
-
Zhaoli Ma and Lin Wang
- Subjects
ALGORITHMS ,STOCHASTIC convergence ,MATHEMATICAL mappings ,HILBERT space ,MATHEMATICAL inequalities - Abstract
The purpose of this paper is to propose an algorithm to solve the split common fixed point problems for total asymptotically strict pseudocontraction mappings in Hilbert spaces. Without the assumption of semi-compactness on the mappings, the iterative scheme is shown to converge strongly to a split common fixed point of such mappings. The results presented in the paper improve and extend some recent corresponding results. [ABSTRACT FROM AUTHOR]
- Published
- 2015
- Full Text
- View/download PDF
32. A viscosity approximation method for weakly relatively nonexpansive mappings by the sunny nonexpansive retractions in Banach spaces.
- Author
-
Chin-Tzong Pang, Naraghirad, Eskandar, and Ching-Feng Wen
- Subjects
APPROXIMATION theory ,NONEXPANSIVE mappings ,BANACH spaces ,ALGORITHMS ,STOCHASTIC convergence - Abstract
In this paper, we introduce a new viscosity approximation method by using the shrinking projection algorithm to approximate a common fixed point of a countable family of nonlinear mappings in a Banach space. Under quite mild assumptions, we establish the strong convergence of the sequence generated by the proposed algorithm and provide an affirmative answer to an open problem posed by Maingé (Comput. Math. Appl. 59:74-79, 2010) for quasi-nonexpansive mappings. In contrast with related processes, our method does not require any demiclosedness principle condition imposed on the involved operators belonging to the wide class of quasi-nonexpansive operators. As an application, we also introduce an iterative algorithm for finding a common element of the set of common fixed points of an infinite family of quasi-nonexpansive mappings and the set of solutions of a mixed equilibrium problem in a real Banach space. We prove a strong convergence theorem by using the proposed algorithm under some suitable conditions. Our results improve and generalize many known results in the current literature. [ABSTRACT FROM AUTHOR]
- Published
- 2015
- Full Text
- View/download PDF
33. A Descent Algorithm-Based Parallel Variable Dual Matrix Model and Application to Blind Source Separation.
- Author
-
Zeng, T.-J. and Feng, Q.-Y.
- Subjects
ALGORITHMS ,BLIND source separation ,COST functions ,COMPUTER simulation ,STOCHASTIC convergence - Abstract
In this paper, we focus on the problem of blind source separation (BSS). To solve the problem efficiently, a new algorithm is proposed. First, a parallel variable dual-matrix model (PVDMM) that considers all the numerical relations between a mixing matrix and a separating matrix is proposed. Different constrained terms are used to construct the cost function for every sub-algorithm. These constrained terms reflect a numerical relation. Therefore, a number of undesired solutions are excluded, the search region is reduced, and the convergence efficiency of the algorithm is ultimately improved. Parallel sub-algorithms are proven to converge to a separable matrix only if the cost function approaches zero. Second, a descent algorithm (DA) as a PVDMM optimizing approach is proposed in this paper as well. Apparently, the efficiency of the algorithm depends completely on the DA. Unlike the traditional descent method, the DA defines step length by solving inequality instead of merely utilizing the Wolfe- or Armijo-type search rule. Stimulation results indicate that the DA can improve computational efficiency. Under mild conditions, the DA has been proven to have strong convergence properties. Numerical results also show that the method is very efficient and robust. Finally, we applied the combinative algorithm to the BSS problem. Computer simulations illustrate its good performance. [ABSTRACT FROM AUTHOR]
- Published
- 2015
- Full Text
- View/download PDF
34. A Progressive Hedging based branch-and-bound algorithm for mixed-integer stochastic programs.
- Author
-
Atakan, Semih and Sen, Suvrajeet
- Subjects
STOCHASTIC programming ,ALGORITHMS ,MIXED integer linear programming ,HEDGING (Finance) ,STOCHASTIC convergence - Abstract
Progressive Hedging (PH) is a well-known algorithm for solving multi-stage stochastic convex optimization problems. Most previous extensions of PH for mixed-integer stochastic programs have been implemented without convergence guarantees. In this paper, we present a new framework that shows how PH can be utilized while guaranteeing convergence to globally optimal solutions of mixed-integer stochastic convex programs. We demonstrate the effectiveness of the proposed framework through computational experiments. [ABSTRACT FROM AUTHOR]
- Published
- 2018
- Full Text
- View/download PDF
35. New general systems of set-valued variational inclusions involving relative (A, η)-maximal monotone operators in Hilbert spaces.
- Author
-
Ting-jian Xiong and Heng-you Lan
- Subjects
MONOTONE operators ,HILBERT space ,STOCHASTIC convergence ,VARIATIONAL inequalities (Mathematics) ,COMPLEMENTARITY constraints (Mathematics) ,ALGORITHMS - Abstract
The purpose of this paper is to introduce and study a class of new general systems of set-valued variational inclusions involving relative (A,η)-maximal monotone operators in Hilbert spaces. By using the generalized resolvent operator technique associated with relative (A,η)-maximal monotone operators, we also construct some new iterative algorithms for finding approximation solutions to the general systems of set-valued variational inclusions and prove the convergence of the sequences generated by the algorithms. The results presented in this paper improve and extend some known results in the literature. [ABSTRACT FROM AUTHOR]
- Published
- 2014
- Full Text
- View/download PDF
36. Weak convergence theorems of a hybrid algorithm in Hilbert spaces.
- Author
-
Yan Hao
- Subjects
STOCHASTIC convergence ,STOCHASTIC processes ,HILBERT space ,BANACH spaces ,ALGORITHMS ,MATHEMATICS theorems - Abstract
In this paper, a hybrid algorithm is investigated for solving common solutions of a generalized equilibrium problem, a variational inequality, and fixed point problems of an asymptotically strict pseudocontraction. Weak convergence theorems are established in the framework of real Hilbert spaces. [ABSTRACT FROM AUTHOR]
- Published
- 2014
- Full Text
- View/download PDF
37. A full-Newton step feasible interior-point algorithm for $$P_*(\kappa )$$ -linear complementarity problems.
- Author
-
Wang, G., Yu, C., and Teo, K.
- Subjects
FEASIBILITY studies ,INTERIOR-point methods ,ALGORITHMS ,LINEAR complementarity problem ,STOCHASTIC convergence ,POLYNOMIALS - Abstract
In this paper, a full-Newton step feasible interior-point algorithm is proposed for solving $$P_*(\kappa )$$ -linear complementarity problems. We prove that the full-Newton step to the central path is local quadratically convergent and the proposed algorithm has polynomial iteration complexity, namely, $$O\left( (1+4\kappa )\sqrt{n}\log {\frac{n}{\varepsilon }}\right) $$ , which matches the currently best known iteration bound for $$P_*(\kappa )$$ -linear complementarity problems. Some preliminary numerical results are provided to demonstrate the computational performance of the proposed algorithm. [ABSTRACT FROM AUTHOR]
- Published
- 2014
- Full Text
- View/download PDF
38. Quantile regression with ℓ-regularization and Gaussian kernels.
- Author
-
Shi, Lei, Huang, Xiaolin, Tian, Zheng, and Suykens, Johan
- Subjects
QUANTILE regression ,MATHEMATICAL regularization ,GAUSSIAN processes ,KERNEL (Mathematics) ,ALGORITHMS ,STOCHASTIC convergence ,ERROR analysis in mathematics ,SAMPLING (Process) - Abstract
The quantile regression problem is considered by learning schemes based on ℓ-regularization and Gaussian kernels. The purpose of this paper is to present concentration estimates for the algorithms. Our analysis shows that the convergence behavior of ℓ-quantile regression with Gaussian kernels is almost the same as that of the RKHS-based learning schemes. Furthermore, the previous analysis for kernel-based quantile regression usually requires that the output sample values are uniformly bounded, which excludes the common case with Gaussian noise. Our error analysis presented in this paper can give satisfactory convergence rates even for unbounded sampling processes. Besides, numerical experiments are given which support the theoretical results. [ABSTRACT FROM AUTHOR]
- Published
- 2014
- Full Text
- View/download PDF
39. Restricted Normal Cones and Sparsity Optimization with Affine Constraints.
- Author
-
Bauschke, Heinz, Luke, D., Phan, Hung, and Wang, Xianfu
- Subjects
MATHEMATICAL optimization ,PROBLEM solving ,PARALLEL computers ,STOCHASTIC convergence ,ALGORITHMS ,ESTIMATION theory - Abstract
The problem of finding a vector with the fewest nonzero elements that satisfies an underdetermined system of linear equations is an NP-complete problem that is typically solved numerically via convex heuristics or nicely behaved nonconvex relaxations. In this paper we consider the elementary method of alternating projections (MAP) for solving the sparsity optimization problem without employing convex heuristics. In a parallel paper we recently introduced the restricted normal cone which generalizes the classical Mordukhovich normal cone and reconciles some fundamental gaps in the theory of sufficient conditions for local linear convergence of the MAP algorithm. We use the restricted normal cone together with the notion of superregularity, which is inherently satisfied for the affine sparse optimization problem, to obtain local linear convergence results with estimates for the radius of convergence of the MAP algorithm applied to sparsity optimization with an affine constraint. [ABSTRACT FROM AUTHOR]
- Published
- 2014
- Full Text
- View/download PDF
40. General split equality problems in Hilbert spaces.
- Author
-
Rudong Chen, Jie Wang, and Huiwen Zhang
- Subjects
HILBERT space ,PROBLEM solving ,CONVEX functions ,ALGORITHMS ,STOCHASTIC convergence ,DIMENSIONAL analysis - Abstract
A new convex feasibility problem, the split equality problem (SEP), has been proposed by Moudafi and Byrne. The SEP was solved through the ACQA and ARCQA algorithms. In this paper the SEPs are extended to infinite-dimensional SEPs in Hilbert spaces and we established the strong convergence of a proposed algorithm to a solution of general split equality problems (GSEPs). [ABSTRACT FROM AUTHOR]
- Published
- 2014
- Full Text
- View/download PDF
41. Convergence theorems for some multi-valued generalized nonexpansive mappings.
- Author
-
Shih-sen Chang, Yong-kun Tang, Lin Wang, Yu-guang Xu, Yun-he Zhao, and Gang Wang
- Subjects
STOCHASTIC convergence ,MATHEMATICS theorems ,SET-valued maps ,GENERALIZATION ,NONEXPANSIVE mappings ,ALGORITHMS ,FIXED point theory - Abstract
In this paper, we propose an algorithms for finding a common fixed point of an infinite family of multi-valued generalized nonexpansive mappings in uniformly convex Banach spaces. Under suitable conditions some strong and weak convergence theorems for such mappings are proved. The results presented in the paper improve and extend the corresponding results of Suzuki (J. Math. Anal. Appl. 340:1088-1095, 2008), Eslamian and Abkar (Math. Comput. Model. 54:105-111, 2011), Abbas et al. (Appl. Math. Lett. 24:97-102, 2011) and others. [ABSTRACT FROM AUTHOR]
- Published
- 2014
- Full Text
- View/download PDF
42. A general iteration scheme for variational inequality problem and common fixed point problems of nonexpansive mappings in q-uniformly smooth Banach spaces.
- Author
-
Song, Yanlai and Ceng, Luchuan
- Subjects
ITERATIVE methods (Mathematics) ,VARIATIONAL inequalities (Mathematics) ,BANACH spaces ,ALGORITHMS ,NONEXPANSIVE mappings ,STOCHASTIC convergence - Abstract
In this paper, we introduce a general iterative algorithm for finding a common element of the set of common fixed points of an infinite family of nonexpansive mappings and the set of solutions of systems of variational inequalities for two inverse strongly accretive mappings in a q-uniformly smooth Banach space. Then, we prove a strong convergence theorem for the iterative sequence generated by the proposed iterative algorithm under very mild conditions. The methods in the paper are novel and different from those in the early and recent literature. Our results can be viewed as improvement, supplementation, development and extension of the corresponding results in some references to a great extent. [ABSTRACT FROM AUTHOR]
- Published
- 2013
- Full Text
- View/download PDF
43. An improved first-order primal-dual algorithm with a new correction step.
- Author
-
Cai, Xingju, Han, Deren, and Xu, Lingling
- Subjects
CORRECTION factors ,STOCHASTIC convergence ,ALGORITHMS ,NUMERICAL analysis ,IMAGE reconstruction ,PROBLEM solving - Abstract
In this paper, we propose a new correction strategy for some first-order primal-dual algorithms arising from solving, e.g., total variation image restoration. With this strategy, we can prove the convergence of the algorithm under more flexible conditions than those proposed most recently. Some preliminary numerical results of image deblurring support that the new correction strategy can improve the numerical efficiency. [ABSTRACT FROM AUTHOR]
- Published
- 2013
- Full Text
- View/download PDF
44. Geometric branch-and-bound methods for constrained global optimization problems.
- Author
-
Scholz, Daniel
- Subjects
GLOBAL optimization ,ALGORITHMS ,PROBLEM solving ,MATHEMATICAL proofs ,STOCHASTIC convergence ,NUMERICAL analysis - Abstract
Geometric branch-and-bound methods are popular solution algorithms in deterministic global optimization to solve problems in small dimensions. The aim of this paper is to formulate a geometric branch-and-bound method for constrained global optimization problems which allows the use of arbitrary bounding operations. In particular, our main goal is to prove the convergence of the suggested method using the concept of the rate of convergence in geometric branch-and-bound methods as introduced in some recent publications. Furthermore, some efficient further discarding tests using necessary conditions for optimality are derived and illustrated numerically on an obnoxious facility location problem. [ABSTRACT FROM AUTHOR]
- Published
- 2013
- Full Text
- View/download PDF
45. Parallel distributed block coordinate descent methods based on pairwise comparison oracle.
- Author
-
Matsui, Kota, Kumagai, Wataru, and Kanamori, Takafumi
- Subjects
MATHEMATICAL optimization ,ALGORITHMS ,COORDINATES ,STOCHASTIC convergence ,ESTIMATION theory - Abstract
This paper provides a block coordinate descent algorithm to solve unconstrained optimization problems. Our algorithm uses only pairwise comparison of function values, which tells us only the order of function values over two points, and does not require computation of a function value itself or a gradient. Our algorithm iterates two steps: the direction estimate step and the search step. In the direction estimate step, a Newton-type search direction is estimated through a block coordinate descent-based computation method with the pairwise comparison. In the search step, a numerical solution is updated along the estimated direction. The computation in the direction estimate step can be easily parallelized, and thus, the algorithm works efficiently to find the minimizer of the objective function. Also, we theoretically derive an upper bound of the convergence rate for our algorithm and show that our algorithm achieves the optimal query complexity for specific cases. In numerical experiments, we show that our method efficiently finds the optimal solution compared to some existing methods based on the pairwise comparison. [ABSTRACT FROM AUTHOR]
- Published
- 2017
- Full Text
- View/download PDF
46. A supplement to a regularization method for the proximal point algorithm.
- Author
-
Saejung, Satit
- Subjects
ITERATIVE methods (Mathematics) ,STOCHASTIC convergence ,APPROXIMATION theory ,ALGORITHMS ,NUMERICAL analysis - Abstract
The purpose of this paper is to show that the iterative scheme recently studied by Xu (J Glob Optim 36(1):115-125, ) is the same as the one studied by Kamimura and Takahashi (J Approx Theory 106(2):226-240, ) and to give a supplement to these results. With the new technique proposed by Maingé (Comput Math Appl 59(1):74-79, ), we show that the convergence of the iterative scheme is established under another assumption. It is noted that if the computation error is zero or the approximate computation is exact, our new result is a genuine generalization of Xu's result and Kamimura-Takahashi's result. [ABSTRACT FROM AUTHOR]
- Published
- 2013
- Full Text
- View/download PDF
47. Conditional quantiles with varying Gaussians.
- Author
-
Xiang, Dao-Hong
- Subjects
GAUSSIAN distribution ,STOCHASTIC convergence ,ALGORITHMS ,LEAST squares ,REGRESSION analysis - Abstract
In this paper we study conditional quantile regression by learning algorithms generated from Tikhonov regularization schemes associated with pinball loss and varying Gaussian kernels. Our main goal is to provide convergence rates for the algorithm and illustrate differences between the conditional quantile regression and the least square regression. Applying varying Gaussian kernels improves the approximation ability of the algorithm. Bounds for the sample error are achieved by using a projection operator, a variance-expectation bound derived from a condition on conditional distributions and a tight bound for the covering numbers involving the Gaussian kernels. [ABSTRACT FROM AUTHOR]
- Published
- 2013
- Full Text
- View/download PDF
48. A discrete PSO for two-stage assembly scheduling problem.
- Author
-
Tian, Ye, Liu, Dayou, Yuan, Donghui, and Wang, Kunhao
- Subjects
PARTICLE swarm optimization ,DISCRETE systems ,COMPUTER scheduling ,ALGORITHMS ,STOCHASTIC convergence ,ELECTRONIC information resource searching ,COMPARATIVE studies - Abstract
In this paper, a discrete particle swarm optimization (PSO) algorithm called DPSO is proposed to solve the two-stage assembly scheduling problem with respect to bicriteria of makespan and mean completion time where setup times are treated as separate from processing times. In DPSO, the particle velocity representation is redefined, and particle movement is modified accordingly. In order to refrain from the shortcoming of premature convergence, individual intensity is defined, which is used to control adaptive mutation of the particle, and mutation mode is decided by the individual fitness. Furthermore, a randomized exchange neighborhood search is introduced to enhance the local search ability of the particle and increase the convergence speed. Finally, the proposed algorithm is tested on different scale problems and compared with the proposed efficient algorithms in the literature recently. The results show that DPSO is an effective and efficient for assembly scheduling problem. [ABSTRACT FROM AUTHOR]
- Published
- 2013
- Full Text
- View/download PDF
49. A pseudo particle swarm optimization for the RCPSP.
- Author
-
Nasiri, Mohammad
- Subjects
PARTICLE swarm optimization ,ALGORITHMS ,PRODUCTION scheduling ,STOCHASTIC convergence ,BENCHMARKING (Management) ,ECONOMIC competition ,ITERATIVE methods (Mathematics) - Abstract
In this paper, a pseudo particle swarm optimization (PSO) algorithm is presented to solve the Resource-Constrained Project Scheduling Problem (RCPSP). The proposed algorithm uses the path relinking procedure as a way for the particles in PSO to fly toward local and global best positions. In order to prevent the premature convergence, a mechanism for maintaining the swarm diversity is used. The pseudo PSO algorithm imposes a distance greater than a threshold between the particles in the swarm. The distance threshold is reduced as the iteration number is increased. Extensive computational experiments were executed on standard benchmark problem sets of PSPLIB. The computational results show that the algorithm outperforms all of the other PSO approaches (known by the authors) applied to RCPSP and for the instance set j30, is competitive with the state of the art meta-heuristics. [ABSTRACT FROM AUTHOR]
- Published
- 2013
- Full Text
- View/download PDF
50. Strong convergence by the shrinking effect of two half-spaces and applications.
- Author
-
Ahmad Khan, Muhammad Aqeel and Fukhar-ud-din, Hafiz
- Subjects
STOCHASTIC convergence ,HILBERT space ,HYBRID systems ,ALGORITHMS ,APPROXIMATION theory ,EQUILIBRIUM - Abstract
This paper provides a new hybrid-type shrinking projection method for strong convergence results in a Hilbert space. The paper continues - by utilizing the proposed hybrid algorithm - with a strong convergence towards an approximate common element of the set of solutions of a finite family of generalized equilibrium problems and the set of common fixed points of two finite families of k-strict pseudo-contractions in a Hilbert space. Comparatively, our results improve and extend various results announced in the current literature. [ABSTRACT FROM AUTHOR]
- Published
- 2013
- Full Text
- View/download PDF
Discovery Service for Jio Institute Digital Library
For full access to our library's resources, please sign in.