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In this paper, first we study the weak convergence of the proximal point algorithm for an infinite family of equilibrium problems of pseudo-monotone type in Hilbert spaces. Then with additional conditions on the bifunctions, we prove the strong convergence for the family to a common equilibrium point. We also study a regularization of Halpern type and prove the strong convergence of the generated sequence to an equilibrium point of the family of infinite pseudo-monotone bifunctions without any additional assumptions on the bifunctions. A concrete example of a family of pseudo-monotone bifunctions is also presented. [ABSTRACT FROM PUBLISHER]

In this paper, we propose adaptive algorithms for parametric identification of discrete systems with lagged variables. For the case with lagged values of input variables, we develop adaptive algorithms and prove their convergence and the boundedness of all trajectories in the adaptive system. The convergence area of an adaptive algorithm depends on the effective perturbation. Models with multiplicative parameters are proposed to reduce the number of evaluated parameters. The procedure of choosing the vector of basic parameters of a such model is developed. The functioning of adaptive identification system is proved for this case. It is shown that if multiplicative identification is applied, the parameters of the evaluation system should be selected from the condition of minimizing the criterion that depends on the prediction error. In the case where lagged variables are interconnected, we propose a transformation which allows one to exclude this mutual influence of variables. The second part of the work is devoted to the analysis of adaptive algorithms for the systems described by equations with the lagged output variable. A linear dependence of the output of the system and the effective perturbation is assumed. Application of adaptive algorithms described in the first part of the work does not make it possible to obtain valid estimates of parameters. We proposed to estimate the existing perturbation for solving the problem. Relevant procedures are described and their functioning is proved. We also present the results of modeling that confirm the functioning of adaptive methods. [ABSTRACT FROM AUTHOR]

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]

This paper proposes an iterative method for solving an operator equation on a separable Hilbert space H equipped with a g-frame. We design an algorithm based on the conjugate gradient method and investigate the convergence and optimality of this algorithm. [ABSTRACT FROM AUTHOR]

The discretetime periodic matrix equations are encountered in periodic state feedback problems and model reduction of periodic descriptor systems. The aim of this paper is to compute the generalized reflexive solutions of the general coupled discretetime periodic matrix equations. We introduce a gradientbased iterative (GI) algorithm for finding the generalized reflexive solutions of the general coupled discrete time periodic matrix equations. It is shown that the introduced GI algorithm always converges to the generalized reflexive solutions for any initial generalized reflexive matrices. Finally, two numerical examples are investigated to confirm the efficiency of GI algorithm. [ABSTRACT FROM PUBLISHER]

In this paper, we introduce a new family of nonstationary refinable functions from Generalized Bernstein Polynomials, which include a class of nonstationary refinable functions generated from the family of masks for the pseudo splines of type II (see [17]). Furthermore, a proof of the convergence of nonstationary cascade algorithms associated with the new masks is completed. We then construct symmetric compacted supported nonstationary C∞ tight wavelet frames in L2(R) with the spectral frame approximation order. [ABSTRACT FROM AUTHOR]

In this paper, a new modified proximal point algorithm involving fixed point iterates of asymptotically nonexpansive mappings in $\operatorname {CAT}(0)$ spaces is proposed and the existence of a sequence generated by our iterative process converging to a minimizer of a convex function and a common fixed point of asymptotically nonexpansive mappings is proved. [ABSTRACT FROM AUTHOR]

This paper introduces a new, fast, efficient and global optimization algorithm called hybrid invasive weed optimization (IWO) and wind driven optimization (WDO). The hybrid algorithm is verified with six standard benchmark functions and implemented to the nulling pattern synthesis of a uniform linear array (ULA) and non-linear circular array (NUCA) antenna having a minimum side lobe level (SLL), and beam width to minimize the interference effect by optimizing the parameters of array elements. Two examples of ULA pattern synthesis with broad null at desired direction are considered to illustrate the efficacy of the proposed algorithm. The results are compared with those obtained by BEES, PGSA, BFO, WDO and MTACO algorithms. Further, one design example of NUCA antenna is considered and the results obtained by hybrid algorithm is compared with those obtained by other evolutionary algorithms such as GA, PSO, CS, FA, BBO, COA, and MIWO. Simulation studies demonstrate the improved performance of hybrid IWO/WDO algorithm in terms of synthesizing broad null, minimum SLL, beam width control and the rate of convergence for nulling pattern synthesis of ULA and NUCA antenna compared to other twelve reported algorithms. [ABSTRACT FROM AUTHOR]

In this paper, a DL-type conjugate gradient method is presented. The given method is a modification of the Dai–Liao conjugate gradient method. It can also be considered as a modified LS conjugate gradient method. For general objective functions, the proposed method possesses the sufficient descent condition under the Wolfe line search and is globally convergent. Numerical comparisons show that the proposed algorithm slightly outperforms the PRP+ and CG-descent gradient algorithms as well as the Barzilai–Borwein gradient algorithm. [ABSTRACT FROM AUTHOR]

In this paper, we revisit the augmented Lagrangian method for a class of nonsmooth convex optimization. We present the Lagrange optimality system of the augmented Lagrangian associated with the problems, and establish its connections with the standard optimality condition and the saddle point condition of the augmented Lagrangian, which provides a powerful tool for developing numerical algorithms: we derive a Lagrange–Newton algorithm for the nonsmooth convex optimization, and establish the nonsingularity of the Newton system and the local convergence of the algorithm. [ABSTRACT FROM PUBLISHER]

In this paper, we study a class of efficient iterative algorithms for the large sparse nonsingular saddle point problems based on the upper and lower triangular (ULT) splitting of the coefficient matrix. We call these algorithms ULT methods. First, the ULT algorithm is established and the characteristic of eigenvalues of the iteration matrix of these new methods is analyzed. Then we give the sufficient and necessary conditions for the convergence of these ULT methods. Moreover, the optimal iteration parameters and the corresponding convergence factors for some special cases of the ULT methods are presented. Numerical experiments on a few model problems are presented to support the theoretical results and examine the numerical effectiveness of these new methods. [ABSTRACT FROM AUTHOR]

Reinforcement learning (RL) is a learning paradigm that can be useful in a wide variety of real-world applications. However, its applicability to complex problems remains problematic due to different causes. Particularly important among these are the high quantity of data required by the agent to learn useful policies and the poor scalability to high-dimensional problems due to the use of local approximators. This paper presents a novel RL algorithm, called online fitted policy iteration (OFPI), that steps forward in both directions. OFPI is based on a semi-batch scheme that increases the convergence speed by reusing data and enables the use of global approximators by reformulating the value function approximation as a standard supervised problem. The proposed method has been empirically evaluated in three benchmark problems. During the experiments, OFPI has employed a neural network trained with the extreme learning machine algorithm to approximate the value functions. Results have demonstrated the stability of OFPI using a global function approximator and also performance improvements over two baseline algorithms (SARSA and Q-learning) combined with eligibility traces and a radial basis function network. [ABSTRACT FROM AUTHOR]

In this paper, inspired by Hussain et al. (Fixed Point Theory Appl. 2015:17, ), we study a modified Mann method to approximate strongly fixed points of strict pseudo-contractive mappings. In (Hussain et al. in Fixed Point Theory Appl. 2015:17, ) it is shown that the same algorithm converges strongly to a fixed point of a nonexpansive mapping under suitable hypotheses on the coefficients. Here the assumptions on the coefficients are different, as well as the techniques of the proof. [ABSTRACT FROM AUTHOR]

Distributed signal processing algorithms have become a hot topic during the past years. One class of algorithms that have received special attention are particles filters (PFs). However, most distributed PFs involve various heuristic or simplifying approximations and, as a consequence, classical convergence theorems for standard PFs do not hold for their distributed counterparts. In this paper, we analyze a distributed PF based on the non-proportional weight-allocation scheme of Bolic et al (2005) and prove rigorously that, under certain stability assumptions, its asymptotic convergence is guaranteed uniformly over time, in such a way that approximation errors can be kept bounded with a fixed computational budget. To illustrate the theoretical findings, we carry out computer simulations for a target tracking problem. The numerical results show that the distributed PF has a negligible performance loss (compared to a centralized filter) for this problem and enable us to empirically validate the key assumptions of the analysis. [ABSTRACT FROM AUTHOR]

This paper presents a new sign subband adaptive filter (SSAF) algorithm with an individual-weighting-factor (IWF) for each subband, instead of a common weighting factor in the original SSAF algorithm, called the IWF-SSAF. Each individual weighting factor only depends on the corresponding subband input signal power. Compared with the SSAF algorithm, the proposed approach fully utilizes the inherent decorrelating property of subband adaptive filter for colored inputs, leading to a better convergence performance. After that, to further enhance the performance of the IWF-SSAF in a sparse system, an improved proportionate IWF-SSAF (IWF-IPSSAF) algorithm is proposed. The proposed algorithms not only inherit the good robustness of sign algorithm against impulsive interferences, but also obtain a significant improvement in the performance as compared to their counterparts (i.e., SSAF and IPSSAF), in terms of the convergence rate and tracking capability. Besides, the IWF-IPSSAF algorithm has faster convergence rate than the IWF-SSAF algorithm for sparse impulse responses. Finally, the performances of two proposed algorithms are demonstrated in the system identification and the acoustic echo cancellation with double-talk. [ABSTRACT FROM AUTHOR]

In this paper, we study a class of weakly nonlinear complementarity problems arising from the discretization of free boundary problems. By reformulating the complementarity problems as implicit fixed-point equations based on splitting of the system matrices, we propose a class of modulus-based matrix splitting algorithms. We show their convergence by assuming that the system matrix is positive definite. Moreover, we give several kinds of typical practical choices of the modulus-based matrix splitting iteration methods based on the different splitting of the system matrix. Numerical experiments on two model problems are presented to illustrate the theoretical results and examine the numerical effectiveness of our modulus-based matrix splitting algorithms. Copyright © 2016 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper deals with the second-order nonlinear neutral delay difference equation Δ(anh(xn-τ1n,xn-τ2n,…,xn-τmn)Δ(xn-qnxn-τ0))+f(n,xn-σ1n,xn-σ2n,…,xn-σkn)=bn, n≥n0. Using the Banach fixed point theorem, Mann iterative method with errors, and some new techniques, we prove the existence of uncountably many positive solutions and the convergence of the sequences generated by the Mann iterative method with errors relative to these solutions for the above equation. Six examples are included. Our results extend and improve essentially the known results in this field. [ABSTRACT FROM AUTHOR]

This paper formulates the PageRank problem A x = x into a consistent singular linear system ( I − A ) x = 0 , and applies the full orthogonalization method (FOM) to solve it. This singular system is characterized by index one, namely i n d e x ( I − A ) = 1 . We analyze the breakdown performance of FOM on a general singular linear system, and conclude that FOM can determine a solution if it converges, without any unfortunate breakdowns for our target problem. Then we propose to use a vector extrapolation method to speed up the convergence performance of FOM. This extrapolation procedure is based on Ritz values, which directly stems from the Arnoldi-Extrapolation algorithm (Wu and Wei, 2010). Eventually numerical experiments are presented to illustrate the effectiveness of our approaches. [ABSTRACT FROM AUTHOR]

In this paper, we propose an algorithm for the solution of nonlinear constrained programming. This algorithm does not use any penalty function or a filter. Instead, it uses the idea of maximal constraint violation to guarantee global convergence. The infeasibility of each iterate is controlled by a progressively decreasing limit. At each iteration, a normal step which is obtained by solving a tightened normal subproblem and a tangential step which is a solution of a tangential subproblem are computed successively. The algorithm reduces the value of objective function or improves feasibility according to the relation of the tangential predicted reduction and the predicted reduction of constraint violation achieved by the trial step. The framework of the algorithm ensures the global convergence without assuming regularity or boundedness of iterate sequence. Moreover, the algorithm does not need any restoration phase. We also include some preliminary yet promising numerical results on some standard test problems in constrained optimization. [ABSTRACT FROM AUTHOR]

Split variational inclusion problem is an important problem, and it is a generalization of the split feasibility problem. In this paper, we present feasible algorithms for the split variational inclusion problems in Hilbert spaces, and provide convergence theorems for these algorithms. As application, we study the split feasibility problem in real Hilbert spaces. Final, numerical results are given for our main results. [ABSTRACT FROM AUTHOR]

In this paper, we first propose a weak convergence algorithm, called the linesearch algorithm, for solving a split equilibrium problem and nonexpansive mapping (SEPNM) in real Hilbert spaces, in which the first bifunction is pseudomonotone with respect to its solution set, the second bifunction is monotone, and fixed point mappings are nonexpansive. In this algorithm, we combine the extragradient method incorporated with the Armijo linesearch rule for solving equilibrium problems and the Mann method for finding a fixed point of an nonexpansive mapping. We then combine the proposed algorithm with hybrid cutting technique to get a strong convergence algorithm for SEPNM. Special cases of these algorithms are also given. [ABSTRACT FROM AUTHOR]

In this paper, a finite filter is used in the structure of the Barzilai–Browein (BB) gradient method in order to propose a new modified BB algorithm for solving large-scale unconstrained optimization problems. Our algorithm is equipped with a relaxed nonmonotone line search technique which allows the algorithm to enjoy the nonmonotonicity properties from scratch. Under some suitable conditions, the global convergence property of the new proposed algorithm is established. Numerical results on some test problems in CUTEr library show the efficiency and effectiveness of the new algorithm in practice too. [ABSTRACT FROM PUBLISHER]

The steady advances of computational methods make model-based optimization an increasingly attractive method for process improvement. Unfortunately, the available models are often inaccurate. The traditional remedy is to update the model parameters, but this generally leads to a difficult parameter estimation problem that must be solved on-line. In addition, the resulting model may not represent the plant well when there is structural mismatch between the two. The iterative optimization method called Modifier Adaptation overcomes these obstacles by directly incorporating plant measurements into the optimization framework, principally in the form of constraint values and cost and constraint gradients. However, the number of experiments required to estimate these gradients increases linearly with the number of process inputs, which tends to make the method intractable for processes with many inputs. This paper presents a new algorithm, called Directional Modifier Adaptation , that overcomes this limitation by only estimating the plant gradients in certain privileged input directions. It is proven that plant optimality with respect to these privileged directions can be guaranteed upon convergence. A novel, statistically optimal, gradient estimation technique is developed. The algorithm is illustrated through the simulation of a realistic airborne wind-energy system, a promising renewable energy technology that harnesses wind energy using large kites. It is shown that Directional Modifier Adaptation can optimize in real time the path followed by the kite. [ABSTRACT FROM AUTHOR]

In industrial applications, many batch/repetitive systems are constructed by two or more subprocesses connected in serial to perform a given task repetitively or periodically, termed as cascaded batch/repetitive processes. In this paper, by introducing a two-dimensional (2D) cost function, an integrated design method of a novel cascade control scheme is developed for this kind of process under the 2D model predictive iterative learning control infrastructure. The resulted cascade control scheme essentially consists of a real-time cascade model predictive control along the time direction as the inner-loop control and an iterative learning control (ILC) along the cycle direction as the outer-loop control. The proposed design algorithm not only realizes an integrated design for all control loops but also guarantees optimal control in terms of the 2D control performance. The convergence criterion of the closed-loop control system along the cycle index is also investigated. Compared to the conventional cascade control schemes, the proposed algorithm is essentially a 2D feedback control with superior control performances which are clearly illustrated by the simulation results on the injection molding process. [ABSTRACT FROM AUTHOR]

In this paper, we propose a new iterative algorithm to approximate fixed point of Suzuki’s generalized nonexpansive mappings. We establish some weak and strong convergence theorems in a uniformly convex Banach space. We also provide examples to illustrate the convergence behavior of the proposed algorithm. [ABSTRACT FROM AUTHOR]

In the matrix completion problem, most methods to solve the nuclear norm model are relaxing it to the nuclear norm regularized least squares problem. In this paper, we propose a new unconstraint model for matrix completion problem based on nuclear norm and indicator function and design a proximal point algorithm (PPA-IF) to solve it. Then the convergence of our algorithm is established strictly. Finally, we report numerical results for solving noiseless and noisy matrix completion problems and image reconstruction. [ABSTRACT FROM AUTHOR]

In this paper we study numerical stability of path-based algorithms for the traffic assignment problem. These algorithms are based on decomposition of the original problem into smaller sub-problems which are optimized sequentially. Previously, path-based algorithms were numerically tested only in the setting of moderate requirements to the level of solution precision. In this study we analyse convergence of these methods when the convergence measure approaches machine epsilon of IEEE double precision format. In particular, we demonstrate that the straightforward implementation of one of the algorithms of this group (projected gradient) suffers from loss of precision and is not able to converge to highly precise solution. We propose a way to solve this problem and test the proposed adjusted version of the algorithm on various benchmark instances. [ABSTRACT FROM AUTHOR]

This paper introduces a novel method to track the global maximum power point (GMPP) under partially shaded conditions (PSCs), for stand-alone photovoltaic (PV) systems. The method combines a new tracking loop based on fuzzy logic controller (FLC) with a scanning and storing algorithm. A Simscape-based PV model working under PSCs is designed and validated experimentally. The developed Simscape-based PV model is mainly used to assess the performance of the proposed method. The simulation results indicate that the developed MPPT method performs better and guarantees an accurate convergence to the GMPP under complicated shading patterns. Furthermore, it provides a fast convergence to the GMPP in rapid transient variation of shading. A comparison study with three recently published MPPT methods have been carried out. It has been shown that the developed method has greatly enhanced the tracking efficiency under PSCs and decrease significantly the response time. Negligible oscillations around the GMPP, system-independent and fast convergence are the main advantages of the proposed method. [ABSTRACT FROM AUTHOR]

In this paper, we develop an error embedded method based on generalized Chebyshev polynomials for solving stiff initial value problems. The solution and the error at each integration step are calculated by generalized Chebyshev polynomials of two consecutive degrees having overlapping zeros, which enables us to minimize overall computational costs. Further the errors at each integration step are embedded in the algorithm itself. In terms of concrete convergence and stability analysis, the constructed algorithm turns out to have the 6th order convergence and an almost L-stability. We assess the proposed method with several numerical results, showing that it uses larger time step sizes and is numerically more efficient. [ABSTRACT FROM AUTHOR]

The sequential block-iterative scheme based on Landweber’s method is a general iterative one for image reconstruction. In this paper, we give the finite termination convergence for this scheme, which provides an approach to choose relaxation coefficients. Furthermore, sufficient and necessary convergence conditions are also established for the sequential block-iterative scheme case. [ABSTRACT FROM AUTHOR]

A trust-region algorithm in association with line search filter technique for solving nonlinear equality constrained programming is proposed in this paper. In the current iteration, the trial step providing sufficient descent is generated by solving a corresponding trust-region subproblem. Then, the step size is decided by backtracking line search together with filter technique to obtain the next iteration point. The advantage of this method is that resolving trust-region subproblem many times to determine a new iteration point in traditional trust-region method can be avoided and hence the expensive computation can be lessened. And the difficult decisions in regard to the choice of penalty parameters in the merit functions can be avoided by using filter technique. Second order correction steps are introduced in the proposed algorithm to overcome Maratos effect. Convergence analysis shows that fast local convergence can be achieved under some mild assumptions. The preliminary numerical results are reported. [ABSTRACT FROM AUTHOR]

A new statistical analysis model is used to analyze the pseudo affine projection (PAP) algorithm with the optimal step-size in this paper. By setting the weight error to be zero in the direction of the adaptive weight update, the optimal step-size is obtained. Two assumptions for the direction vector are proposed, which simplify the analysis of the convergence behavior for the optimal step-size PAP algorithm. Under this condition, deterministic recursive equations for the weight error and for the mean-square error are derived in the direction of the adaptive weight update. Simulation results are provided to corroborate the analytical results. [ABSTRACT FROM AUTHOR]

Due to the strong edge preserving ability and low computational cost, the total variation (TV) regularization has been developed as one promising approach to solve the multiplicative denoising problem. In recent years, many efficient algorithms have been proposed for computing the numerical solution of TV-based convex variational models. Among these methods, the (linearized) augmented Lagrangian algorithm (ALM) and the primal–dual hybrid gradient (PDHG) algorithm are two of the most effective and most widely used techniques. In this paper, inspired by the connection of the ALM and PDHG algorithms, we develop an improved primal–dual algorithm for multiplicative noise removal. In the proposed algorithm, an auxiliary variable, which is updated by the Gauss–Seidel scheme, is introduced to accelerate the original primal–dual framework. The global convergence property of the proposed algorithm is also investigated. Numerical experiments on the multiplicative denoising show that the proposed algorithm outperforms the current state-of-the-art methods. [ABSTRACT FROM AUTHOR]

Global Krylov subspace methods are among the most efficient algorithms to solve matrix equation A X = B . Deflation and augmentation techniques are used to accelerate the convergence of Krylov subspace methods. There are two different approaches for deflated and augmented methods: an augmentation space is applied explicitly in every step, or the global method is used for solving a projected problem and then a correction step is applied at the end. In this paper, we present a framework of deflation and augmentation approaches for accelerating the convergence of the global methods for the solution of nonsingular linear matrix equations A X = B . Then, we define deflated and augmented global algorithms. Also, we analyze the deflated and augmented global minimal residual and global orthogonal residual methods. Finally, we present numerical examples to illustrate the effectiveness of different versions of the new algorithms. [ABSTRACT FROM AUTHOR]

In this paper, we study the consistence of a recurrent stochastic algorithm under quasi-associated random errors. Kholev's algorithm estimates an unknown non-zero parameter θ introduced in a nonlinear autoregressive model. We establish the complete convergence and deduce a confidence interval for θ . [ABSTRACT FROM AUTHOR]

In this paper, we investigate and analyze a proximal point algorithm via viscosity approximation method with error. This algorithm is introduced for finding a common zero point for a countable family of inverse strongly accretive operators and a countable family of nonexpansive mappings in Banach spaces. Our result can be extended to some well known results from a Hilbert space to a uniformly convex and 2−uniformly smooth Banach space. Finally, we establish the strong convergence theorems for the proximal point algorithm. Also, some illustrative numerical examples are presented. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a Halpern's type method to approximate common fixed points of a nonexpansive mappingTand a strongly quasi-nonexpansive mappingsS, defined in a Hilbert space, such thatI − Sis demiclosed at 0. The result shows as the same algorithm converges to different points, depending on the assumptions of the coefficients. Moreover, a numerical example of our iterative scheme is given. [ABSTRACT FROM AUTHOR]

In this paper, we extend the wavelet collocation method to a class of three-dimensional Hammerstein equation with weakly singular kernel. Three-dimensional wavelets and collocation polynomials on the unit cube are constructed. A fast wavelets collocation method is obtained by the use of a practical block truncation strategy. Numerical results are also included. [ABSTRACT FROM PUBLISHER]

In this paper we study new algorithmic structures with Douglas-Rachford (DR) operators to solve convex feasibility problems. We propose to embed the basic two-set-DR algorithmic operator into the string-averaging projections and into the block-iterative projection algorithmic structures, thereby creating new DR algorithmic schemes that include the recently proposed cyclic DR algorithm and the averaged DR algorithm as special cases. We further propose and investigate a new multiple-set-DR algorithmic operator. Convergence of all these algorithmic schemes is studied by using properties of strongly quasi-nonexpansive operators and firmly nonexpansive operators. [ABSTRACT FROM AUTHOR]

The alternating direction method of multipliers (ADMM) is widely used to solve large-scale linearly constrained optimization problems, convex or nonconvex, in many engineering fields. However there is a general lack of theoretical understanding of the algorithm when the objective function is nonconvex. In this paper we analyze the convergence of the ADMM for solving certain nonconvex consensus and sharing problems. We show that the classical ADMM converges to the set of stationary solutions, provided that the penalty parameter in the augmented Lagrangian is chosen to be sufficiently large. For the sharing problems, we show that the ADMM is convergent regardless of the number of variable blocks. Our analysis does not impose any assumptions on the iterates generated by the algorithm and is broadly applicable to many ADMM variants involving proximal update rules and various flexible block selection rules. [ABSTRACT FROM AUTHOR]

This paper develops a new framework to analyze and design iterative optimization algorithms built on the notion of integral quadratic constraints (IQCs) from robust control theory. IQCs provide sufficient conditions for the stability of complicated interconnected systems, and these conditions can be checked by semidefinite programming. We discuss how to adapt IQC theory to study optimization algorithms, proving new inequalities about convex functions and providing a version of IQC theory adapted for use by optimization researchers. Using these inequalities, we derive numerical upper bounds on convergence rates for the Gradient method, the Heavy-ball method, Nesterov's accelerated method, and related variants by solving small, simple semidefinite programming problems. We also briefly show how these techniques can be used to search for optimization algorithms with desired performance characteristics, establishing a new methodology for algorithm design. [ABSTRACT FROM AUTHOR]

In this paper, we study algorithms for Toeplitz matrix recovery. Inspired by the singular value thresholding (SVT) algorithm for matrix completion and the alternating directions iterative method, we first propose a new mean value algorithm for Toeplitz matrix recovery. Then we apply our idea to the augmented Lagrange multiplier (ALM) algorithm for matrix recovery and put forward four modified ALM algorithms for Toeplitz matrix recovery. Convergence analysis of the new algorithms is discussed. All the iterative matrices generated by the five algorithms keep a Toeplitz structure that ensures the fast singular value decomposition (SVD) of Toeplitz matrices. Compared with the original algorithms, our algorithms are far superior in the time of SVD, as well as the CPU time. [ABSTRACT FROM AUTHOR]

We propose a new primal-dual interior-point predictor-corrector algorithm in Ai and Zhang's wide neighborhood for solving monotone linear complementarity problems (LCP). Based on the understanding of this neighborhood, we use two new directions in the predictor step and in the corrector step, respectively. Especially, the use of new corrector direction also reduces the duality gap in the corrector step, which has good effects on the algorithm's convergence. We prove that the new algorithm has a polynomial complexity of , which is the best complexity result so far. In the paper, we also prove a key result for searching for the best step size along some direction. Considering local convergence, we revise the algorithm to be a variant, which enjoys both complexity of and Q-quadratical convergence. Finally, numerical result shows the effectiveness and superiority of the two new algorithms for monotone LCPs. [ABSTRACT FROM AUTHOR]

This paper proposes a new motion planning algorithm for robot manipulator systems with path constraints. The constraint function of a manipulator determines the subspace of its joint space, and a proposed sampling-based algorithm can find a path that connects valid samples in the subspace. These valid samples can be obtained by projecting the samples onto the subspace defined by the constraint function. However, these iteratively generated samples easily fall into local optima, which degrades the search performance. The proposed algorithm uses the local geometric information and expands the search tree adaptively to avoid the local convergence problem. It increases the greediness of the search tree when it expands toward an unexplored area, which produces the benefit of reducing computational time. In order to demonstrate the performance of the algorithm, it is applied to two example problems: a maze problem using PUMA 560 under predefined constraints and a closed-chain problem using two Selective Compliance Assembly Robot Arms. The results are compared with those obtained with an existing algorithm to show the improvement in performance. [ABSTRACT FROM AUTHOR]

In a graph or a network , a set is a dominating set if each node in is adjacent to at least one node in . A dominating set is called minimal when there does not exist a node such that the set is a dominating set. In this paper, we propose a new self-stabilizing algorithm for minimal dominating set. It has safe convergence property under synchronous daemon in the sense that starting from an arbitrary state, it quickly converges to a dominating set (a safe state) in two rounds, and then stabilizes in a minimal dominating set (the legitimate state) in rounds without breaking safety during the convergence interval, where n is the number of nodes. Space requirement at each node is bits. [ABSTRACT FROM AUTHOR]

In this paper, we consider the problem of convergence of an iterative algorithm for a general system of variational inequalities, a nonexpansive mapping and an η-strictly pseudo-contractive mapping. Strong convergence theorems are established in the framework of real Banach spaces. [ABSTRACT FROM AUTHOR]