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In this paper, we present a feasible predictor-corrector interior-point method for symmetric cone optimization problem in the large neighbourhood of the central path. The method is generalization of Ai-Zhang's predictor-corrector algorithm to the symmetric cone optimization problem. Starting with a feasible point in given large neighbourhood of the central path, the algorithm still terminates in at most iterations. This matches the best known iteration bound that is usually achieved by short-step methods, thereby, closing the complexity gap between long- and short-step interior-point methods for symmetric cone optimization. The preliminary numerical results on a selected set of NETLIB problems show advantage of the method in comparison with the version of the algorithm that is not based on the predictor-corrector scheme. [ABSTRACT FROM AUTHOR]

Concave knapsack problems with integer variables have many applications in real life, and they are NP-hard. In this paper, an exact and efficient algorithm is presented for concave knapsack problems. The algorithm combines the contour cut with a special cut to improve the lower bound and reduce the duality gap gradually in the iterative process. The lower bound of the problem is obtained by solving a linear underestimation problem. A special cut is performed by exploiting the structures of the objective function and the feasible region of the primal problem. The optimal solution can be found in a finite number of iterations, and numerical experiments are also reported for two different types of concave objective functions. The computational results show the algorithm is efficient. [ABSTRACT FROM AUTHOR]

This paper develops a parameter estimation algorithm for linear continuous-time systems based on the hierarchical principle and the parameter decomposition strategy. Although the linear continuous-time system is a linear system, its output response is a highly nonlinear function with respect to the system parameters. In order to propose a direct estimation algorithm, a criterion function is constructed between the response output and the observation output by means of the discrete sampled data. Then a scheme by combining the Newton iteration and the least squares iteration is builded to minimise the criterion function and derive the parameter estimation algorithm. In light of the different features between the system parameters and the output function, two sub-algorithms are derived by using the parameter decomposition. In order to remove the associate terms between the two sub-algorithms, a Newton and least squares iterative algorithm is deduced to identify system parameters. Compared with the Newton iterative estimation algorithm without the parameter decomposition, the complexity of the hierarchical Newton and least squares iterative estimation algorithm is reduced because the dimension of the Hessian matrix is lessened after the parameter decomposition. The experimental results show that the proposed algorithm has good performance. [ABSTRACT FROM AUTHOR]

In order to realize accurate control of underwater vehicles, this paper proposed a fractal prediction model of surge. Firstly, we introduce the current state-of-the-art of fractal prediction; secondly, we complete a fractal analysis with the R_S method, calculating the fractal dimension of surge using the short-time dimension method; thirdly, we correct the vertical scaling factor of the Iterated Function System (IFS) using the fractal dimension. Then the predictive value can be calculated through anti-iteration according to the statistical significantly IFS and proposing a fractal prediction model. Finally, we complete a simulation analysis based on the actual data and a comparison to another prediction algorithm. The result shows that the fractal prediction algorithm of this article has better comprehensive performance. [ABSTRACT FROM PUBLISHER]

In this paper, iterative algorithm for strong vector equilibrium problem (SVEP) is studied. Firstly, an auxiliary problem for SVEP is introduced and the relationships between these two problems are discussed. Then, based on the auxiliary problem, a projection iterative algorithm for SVEP is proposed. Moreover, analysis of convergence of this iterative algorithm is investigated under suitable conditions of continuity and convexity. The main result obtained in this paper generalizes and improves the corresponding ones of Iusem and Sosa [Iusem AN, Sosa W. Iterative algorithms for equilibrium problems. Optimization. 2003;52(3):301–316.] and Cheng and Liu [Cheng B, Liu SY. An iterative algorithm for vector equilibrium problems. J. Lanzhou Univ. (Nat. Sci.). 2009;45(5):105–109.]. [ABSTRACT FROM AUTHOR]

The Cauchy problem for the Helmholtz equation is considered. It was demonstrated in a previous paper by the authors that the alternating algorithm suggested by V.A. Kozlov and V.G. Maz’ya does not converge for large wavenumbers k in the Helmholtz equation. Here, we present some simple modifications of the algorithm which may restore the convergence. They consist of the replacement of the Neumann-Dirichlet iterations by the Robin-Dirichlet ones which repairs the convergence for less than the first Dirichlet-Laplacian eigenvalue. In order to treat large wavenumbers, we present an algorithm based on iterative solution of Robin-Dirichlet boundary value problems in a sufficiently narrow border strip. Numerical implementations obtained using the finite difference method are presented. The numerical results illustrate that the algorithms suggested in this paper, produce convergent iterative sequences. [ABSTRACT FROM AUTHOR]

Recently, Salkuyeh and Fahim [A new iterative refinement of the solution of ill-conditioned linear system of equations, Int. Comput. Math. 88(5) (2011), pp. 950–956] have proposed a two-step iterative refinement of the solution of an ill-conditioned linear system of equations. In this paper, we first present a generalized two-step iterative refinement procedure to solve ill-conditioned linear system of equations and study its convergence properties. Afterward, it is shown that the idea of an orthogonal projection technique together with a basic stationary iterative method can be utilized to construct a new efficient and neat hybrid algorithm for solving the mentioned problem. The convergence of the offered hybrid approach is also established. Numerical examples are examined to demonstrate the feasibility of proposed algorithms and their superiority to some of existing approaches for solving ill-conditioned linear system of equations. [ABSTRACT FROM PUBLISHER]

This paper presents a method for determining the optimum number, impedance, and locations of fault current limiter (FCL) to reduce the negative impact of distributed generations presence in the power systems such as increasing the short circuit current levels and improve the system reliability. In the considered method, we have modeled the FCL placement as an optimization problem while the objectives are; bus fault current difference, reliability, the number and impedance of FCLs. Moreover, to solve the proposed problem, a new multi-objective optimization algorithm based on firework algorithm namely multi-objective firework algorithm has been implemented. In the new algorithm, several iterations have been considered, and the non-dominated solutions are extracted and stored in an external repository in the iterations. Finally, a fuzzy clustering technique is used to control the size of the repository during the algorithm evolution. The proposed approach is tested on two different systems, namely, Roy Billinton Test System (RBTS) 2 and RBTS 4 test system. The obtained results demonstrate the effectiveness and feasibility of the new method. [ABSTRACT FROM PUBLISHER]

In this paper,we propose a new predictor–corrector interior-point method for symmetric cone programming. This algorithm is based on a wide neighbourhood and the Nesterov–Todd direction. We prove that, besides the predictor steps, each corrector step also reduces the duality gap by a rate of, whereris the rank of the associated Euclidean Jordan algebras. In particular, the complexity bound is, whereis a given tolerance. To our knowledge, this is the best complexity result obtained so far for interior-point methods with a wide neighbourhood over symmetric cones. The numerical results show that the proposed algorithm is effective. [ABSTRACT FROM AUTHOR]

In this paper, the nonlinear iterative methods, which are different from the classical algorithms, to solve inverse problems are presented. Our methods by denoting some parameters and some properties of the algorithm in both noise and noiseless cases are studied. Finally, the convergence of the sequence generated by the algorithm without noise is discussed. [ABSTRACT FROM AUTHOR]

The consensus reaching process is a dynamic and iterative process for improving group's consensus level before making a final decision in group decision-making (GDM). As the experts will express their opinions under their own intellectual level from different aspects, it is natural that the experts’ weights should reflect their judgment information. This paper proposes a dynamic way to adjust weights of decision-makers (DMs) automatically when they are asked to give original judgment information for GDM problems, in which the DMs express their judgment information by hesitant fuzzy preference relations (HFPRs). Two indices, an individual consensus index of hesitant fuzzy preference relation (ICIHFPR) and a group consensus index of hesitant fuzzy preference relation (GCIHFPR), are introduced. Normalisation of HFPRs with different numbers of possible values is taken into consideration for better computation and comparison. An iterative consensus reaching algorithm is presented with DMs’ weighting vector changing in each consensus reaching process and the process terminates until both theICIHFPRandGCIHFPRare controlled within predefined thresholds. Finally, an example is illustrated and comparative analyses demonstrate the effectiveness of the proposed methods. [ABSTRACT FROM AUTHOR]

In this paper, we present a predictor-corrector infeasible-interior-point method for symmetric cone linear complementarity problem (SCLCP) with the Cartesian-property (-SCLCP). This method is based on a wide neighbourhood, which is an even wider neighbourhood than the negative infinity neighbourhood. We show that the iteration-complexity bound of the proposed algorithm for a commutative class of search directions is, whereis the condition number of matrixG,is the handicap of the problem,ris the rank of the associated Euclidean Jordan algebra andis a given tolerance. To our knowledge, this is the best complexity result obtained so far for the wide neighbourhood infeasible-interior-point methods for the Cartesian-SCLCPs. [ABSTRACT FROM PUBLISHER]

In this paper, we investigate the problem of stability analysis for linear delta operator systems subject to state saturation. Both full state saturation and partial state saturation are investigated for the delta operator systems. Two equivalent necessary and sufficient conditions are identified such that the system with full state saturation is globally asymptotically stable. Based on the sufficient conditions, an iterative algorithm is proposed for testing global asymptotic stability of the system with full state saturation. A new globally asymptotically stable condition is also proposed for the partial state saturation system. Two numerical examples on a ball and beam model are given to show the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the notion of weak sharpness for set-valued variational inequalities in then-dimensional Euclidean space and then present some characterizations of weak sharpness. We also give some examples to illustrate this notion. Under the assumption of weak sharpness, by using the inner limit of a set sequence we establish a sufficient and necessary condition to guarantee the finite termination of an arbitrary algorithm for solving a set-valued variational inequality involving maximal monotone mappings. As an application, we show that the sequence generated by the hybrid projection-proximal point algorithm proposed by Solodov and Svaiter terminates at solutions in a finite number of iterations. These obtained results extend some known results of classical variational inequalities. [ABSTRACT FROM PUBLISHER]

In this paper, we suggest two new iterative methods for finding an element of the solution set of split variational inclusion problem in real Hilbert spaces. Under suitable conditions, we present weak and strong convergence theorems for these methods. We also apply the proposed algorithms to study the split feasibility problem. Finally, we give some numerical results which show that our proposed algorithms are efficient and implementable from the numerical point of view. [ABSTRACT FROM AUTHOR]

H-matrices play an important role in applied sciences such as numerical analysis and optimization theory. An attractive question is to identify whether a given matrix is an H-matrix. In this paper, we propose a new iterative algorithm for identifying H-matrices. We show that the proposed algorithm has linear convergence and can determine the H-matrix characterization for any given matrix. Its performance is illustrated in a set of numerical tests. [ABSTRACT FROM AUTHOR]

The self-updating process (SUP) is a clustering algorithm that stands from the viewpoint of data points and simulates the process how data points move and perform self-clustering. It is an iterative process on the sample space and allows for both time-varying and time-invariant operators. By simulations and comparisons, this paper shows that SUP is particularly competitive in clustering (i) data with noise, (ii) data with a large number of clusters, and (iii) unbalanced data. When noise is present in the data, SUP is able to isolate the noise data points while performing clustering simultaneously. The property of the local updating enables SUP to handle data with a large number of clusters and data of various structures. In this paper, we showed that the blurring mean-shift is a static SUP. Therefore, our discussions on the strengths of SUP also apply to the blurring mean-shift. [ABSTRACT FROM AUTHOR]

In this paper, we propose a non-monotone line search method for solving optimization problems on Stiefel manifold. The main novelty of our approach is that our method uses a search direction based on a linear combination of descent directions and a Barzilai-Borwein line search. The feasibility is guaranteed by projecting each iterate on the Stiefel manifold through SVD (singular value decomposition) factorizations. Some theoretical results for analysing the algorithm are presented. Finally, we provide numerical experiments for comparing our algorithm with other state-of-the-art procedures. The code is available online. The experimental results show that the proposed algorithm is competitive with other approaches and for particular problems, the computational performance is better than the state-of-the-art algorithms. [ABSTRACT FROM AUTHOR]

In this paper we extend the stability and stabilizability concepts from the case that the variables are positive real numbers to the case that the variables are positive linear operators. Since the algebra of bounded linear operators is not commutative, such extension does not appear to be obvious. As applications, iterative operator algorithms, converging to some operator means, are discussed. [ABSTRACT FROM PUBLISHER]

In this paper, we report the experimental implementation of handling the reconstruction problem from few angle data-sets for digital holographic microtomography. First, the digital holographic microscopy with sample-rotating scheme is established and few holograms with regularly spaced angle steps are recorded. Then, an algebraic iterative reconstruction algorithm with non-positivity constraint and a smoothing operator is applied to reconstruct three-dimensional refractive index distribution of the measured sample from the few angle data-sets. The experimental results demonstrate that the algebraic iterative technique can accurately reconstruct refractive index distribution from few angle data-sets in digital holographic microtomography. The technique is easy to implement and reduces greatly the required recording times. [ABSTRACT FROM AUTHOR]

In this paper, we present a novel class of iterative reconstruction methods for severely angular undersampled or/and limited-view tomographic problems with fan-beam scanning geometry. The proposed algorithms are based on a new analytical transform which generalizes Fourier-slice theorem to divergent-beam scanning geometries. Using a non-rigid coordinate transform, divergent rays can be reorganized into parallel ones. Therefore, one can employ a simpler parallel-beam projection model instead of more complicated divergent-beam geometries. Various existing iterative reconstruction techniques for divergent-beam geometries can be easily adapted to the proposed framework. The significant advantage of this formulation is the possibility of exploiting efficient Fourier-based recovery methods without rebinning of the projections. In case of highly sparse measurements (few-view data), rebinning methods are not suitable due to error-prone angular interpolation involved. In this work, three new methods based on the novel analytical framework for fan-beam geometry are presented: the Gerchberg-Papoulis algorithm, the Neumann decomposition method and its total variation regularized version. Presented numerical experiments demonstrate that the methods can be competitive in reconstructing from few-view noisy tomographic measurements. [ABSTRACT FROM AUTHOR]

In this paper, an iterative algorithm for solving the strong vector equilibrium problem with variable domination structure (VSVEP) is considered. First, an auxiliary problem for the VSVEP is introduced and the relationships between the auxiliary problem and VSVEP are discussed. Then, using the auxiliary principle technique, a projection iterative algorithm to compute the approximate solutions of the VSVEP is proposed and analysed. Furthermore, convergence of the iterative sequences generated by this algorithm is investigated under suitable conditions of continuity and convexity. These results extend and improve some recent works in this field. [ABSTRACT FROM AUTHOR]

Recently, Tang et al. [Numer Algorithms. 2014;66(2):379-397] have offered a cyclic iterative method for determining the unique solution of the coupled matrix equations AiXBi = Fi, i = 1, 2,..., N. Analogues to the gradient-based algorithm, the proposed algorithm relies on a fixed parameter whereas it has wider convergence region. Nevertheless, the application of the algorithm to find the centrosymmetric solution of the mentioned problem has been left as a project to be investigated and the optimal value for the fixed parameter has not been derived. In this paper, we focus on a more general class of the coupled linear matrix equations that incorporate the mentioned ones in the earlier refereed work. More precisely, we first develop the authors' propounded algorithm to resolve our considered coupled linear matrix equations over centro-symmetric matrices. Afterwards, we disregard the restriction of the existence of the unique (centro-symmetric) solution and also modify the authors' algorithm by applying an oblique projection technique which allows to produce a sequence of approximate solutions which gratify an optimality property. Numerical results are reported to confirm the validity of the established results and to demonstrate the superior performance of the modified version of the cyclic iterative algorithm. [ABSTRACT FROM AUTHOR]

The coupled-cluster (CC) method is one of the most efficient approaches to describe electron correlation effects in atoms and molecules. The method can be related to other earlier and more conventional methods for an approximate evaluation of the correlation energy like perturbation theory or configuration interaction method. The relations are usually used to suggest possible ways of solving the CC equations. The most popular iterative schemes for obtaining the cluster amplitudes are based on perturbative Jacobi-type procedures but also other algorithms are known from the literature. All of them are characterised by different convergence properties. In the paper, we try to study the efficiency of the basic iterative schemes used in the CC calculations. [ABSTRACT FROM PUBLISHER]

Iterative re-weighted least square (IRLS) algorithms for-minimization problems require to select proper value of regularization parameter, for which Stein’s unbiased risk estimate (SURE) – an unbiased estimate of prediction error – is often used as a criterion for this selection. In this paper, we propose a recursive SURE to estimate the prediction error during the IRLS iterations. Particularly, we derive the recursion of Jacobian matrix by incorporating matrix splitting scheme into IRLS algorithms. Numerical examples demonstrate that minimizing SURE consistently leads to the nearly optimal reconstructions in terms of prediction error. Theoretical derivations in this work related to the evaluation of Jacobian matrix can be extended, in principle, to other types of regularizers and regularized iterative reconstruction algorithms. [ABSTRACT FROM AUTHOR]

Pattern formation is one of the many applications of diffractive optical elements (DOEs) for display. Since DOEs have lightweight and slim nature compared to other optical devices, using them as image projection device in virtual keyboards is suggested. In this paper, we present an approach to designing elements that produce distinct intensity patterns, in the far field, for two wavelengths. These two patterns are images of bilingual virtual keyboard. To achieve this with DOEs is not simple, as they are inherently wavelength specific. Our technique is based on phase periodic characteristic of wavefront using iterative algorithm to design the phase profiles. [ABSTRACT FROM AUTHOR]

In this paper, we propose a new simultaneous iterative algorithm for solving the split common fixed point problem of directed operators. Inspired by the idea of cyclic iterative algorithm, we also introduce two iterative algorithms which combine the process of cyclic and simultaneous together. Under mild assumptions, we prove convergence of the proposed iterative sequences. As applications, we obtain several iteration schemes to solve the inverse problem of multiple-sets split feasibility problem. Numerical experiments are presented to confirm the efficiency of the proposed iterative algorithms. [ABSTRACT FROM AUTHOR]

Let,andbe real Hilbert spaces, letandbe two bounded linear operators. Moudafi introduced simultaneous iterative algorithms with weak convergence for the following split common fixed-point problem:Section.Displaywhereandare two firmly quasi-nonexpansive operators with nonempty fixed-point setsand. Note that, by takingand, we recover the split common fixed-point problem originally introduced by Cesnor and Segal. However, to employ Moudafi’s algorithms, one needs to know a prior norm (or at least an estimate of the norm) of the bounded linear operators. To estimate the norm of an operator is very difficult, if it is not an impossible task. In this paper, we will continue to consider the split common fixed-point problem (1) governed by the general class of quasi-nonexpansive operators. We introduce a simultaneous iterative algorithm with a way of selecting the stepsizes such that the implementation of the algorithm does not need any prior information about the operator norms. The weak convergence result of algorithm is obtained and some applied nonlinear analysis examples are stated. [ABSTRACT FROM AUTHOR]

Bregman iterative algorithms have been extensively used forand total variation regularization problems, allowing to obtain simple, fast and effective algorithms. In this paper, three already-available algorithms for geosounding inversion are modified by including them in a Bregman iterative procedure. The resulting algorithms are easy to implement and do not require any optimization package. Modelling results are presented for synthetic and field data, observing better convergence properties than the original versions, avoiding the need of any continuation descent procedure. [ABSTRACT FROM AUTHOR]

In this paper, we propose variants of Forward-Backward splitting method for finding a zero of the sum of two operators. A classical modification of Forward-Backward method was proposed by Tseng, which is known to converge when the forward and the backward operators are monotone and with Lipschitz continuity of the forward operator. The conceptual algorithm proposed here improves Tseng’s method in some instances. The first and main part of our approach, contains an explicit Armijo-type search in the spirit of the extragradient-like methods for variational inequalities. During the iteration process, the search performs only one calculation of the forward-backward operator in each tentative of the step. This achieves a considerable computational saving when the forward-backward operator is computationally expensive. The second part of the scheme consists in special projection steps. The convergence analysis of the proposed scheme is given assuming monotonicity on both operators, without Lipschitz continuity assumption on the forward operator. [ABSTRACT FROM AUTHOR]

In this paper, we consider the following minimization problem:where,,,andare given. An efficient inequality relaxation technique is presented to relax the matrix inequality constraint so that there is an optimal solution which is(R,S)-symmetric that minimize, and also satisfies the corrected matrix inequality constraint. A hybrid algorithm with convergence analysis is given to solve this problem. Numerical examples show that the algorithm requires less CPU times when compared with some other methods. [ABSTRACT FROM AUTHOR]

This paper is devoted to the robust finite-time output consensus problems of multi-agent systems under directed graphs, where all agents and their communication topologies are subject to interval uncertainties. Distributed protocols are constructed by using iterative learning control (ILC) algorithms, where information is exchanged only at the end of one iteration and learning is used to update the control inputs after each iteration. It is proved that under ILC-based protocols, the finite-time consensus can be achieved with an increasing number of iterations if the communication network of agents is guaranteed to have a spanning tree. Moreover, if the information of any desired terminal output is available to a portion (not necessarily all) of the agents, then the consensus output that all agents finally reach can be enabled to be the desired terminal output. It is also proved that for all ILC-based protocols, gain selections can be provided in terms of bound values, and consensus conditions can be developed associated with bound matrices. Simulation results are given to demonstrate the effectiveness of our theoretical results. [ABSTRACT FROM AUTHOR]

The explosive growth of the World Wide Web leads to the fast advancing development of e-commerce techniques. Recommender systems, which use personalised information filtering techniques to generate a set of items suitable to a given user, have received considerable attention. User- and item-based algorithms are two popular techniques for the design of recommender systems. These two algorithms are known to have Cold-Start problems, i.e., they are unable to effectively handle Cold-Start users who have an extremely limited number of purchase records. In this paper, we develop TrustRank, a novel recommender system which handles the Cold-Start problem by leveraging the user-trust networks which are commonly available for e-commerce applications. A user-trust network is formed by friendships or trust relationships that users specify among them. While it is straightforward to conjecture that a user-trust network is helpful for improving the accuracy of recommendations, a key challenge for using user-trust network to facilitate Cold-Start users is that these users also tend to have a very limited number of trust relationships. To address this challenge, we propose a pre-processing propagation of the Cold-Start users’ trust network. In particular, by applying the personalised PageRank algorithm, we expand the friends of a given user to include others with similar purchase records to his/her original friends. To make this propagation algorithm scalable to a large amount of users, as required by real-world recommender systems, we devise an iterative computation algorithm of the original personalised TrustRank which can incrementally compute trust vectors for Cold-Start users. We conduct extensive experiments to demonstrate the consistently improvement provided by our proposed algorithm over the existing recommender algorithms on the accuracy of recommendations for Cold-Start users. [ABSTRACT FROM AUTHOR]

In this paper, we propose hybrid implicit and explicit viscosity iterative algorithms for solving general hierarchical fixed-point problems for a countable family of non-expansive mappings in uniformly smooth Banach spaces. These hybrid viscosity algorithms are based on the well-known viscosity approximation method and hybrid steepest-descent method. We obtain some strong convergence theorems under suitable conditions. Our results extend, improve, supplement and develop the recent results in the literature. [ABSTRACT FROM PUBLISHER]

The paper presents the iterative solutions of two coefficient inverse problems (CIPs) arising in frequency sounding and electrical prospecting. An iterative algorithm is constructed to obtain such solutions. Exploiting the Beilina–Klibanov approach to CIPs, this algorithm possesses the new iterative and refinement procedures. These features enhance significantly both the spatial and contrast resolutions of reconstructed coefficients. The computational effectiveness of the proposed numerical technique is demonstrated in computational experiments with two applied CIPs: electromagnetic or acoustic frequency sounding and electrical prospecting of layered media. The Slichter–Langer–Tikhonov formulation is exploited as a mathematical model of the latter. [ABSTRACT FROM PUBLISHER]

This paper presents a new hybrid algorithm for unconstrained optimization problems, which combines the idea of the IMPBOT algorithm with the nonmonotone line search technique. A feature of the proposed method is that at each iteration, a system of linear equations is solved only once to obtain a trial step, via a modified limited-memory BFGS two loop recursion that requires only matrix–vector products, thus reducing the computations and storage. Furthermore, when the trial step is not accepted, the proposed method performs a line search along it using a modified nonmonotone scheme, thus a larger stepsize can be yielded in each line search procedure. Under some reasonable assumptions, the convergence properties of the proposed algorithm are analysed. Numerical results are also reported to show the efficiency of this proposed method. [ABSTRACT FROM PUBLISHER]

In this paper, we propose a trust-region algorithm in association with line search filter technique for solving nonlinear equality constrained programming. At current iteration, a trial step is formed as the sum of a normal step and a tangential step which is generated by trust-region subproblem and the step size is decided by interior backtracking line search together with filter methods. Then, the next iteration is determined. This is different from general trust-region methods in which the next iteration is determined by the ratio of the actual reduction to the predicted reduction. The global convergence analysis for this algorithm is presented under some reasonable assumptions and the preliminary numerical results are reported. [ABSTRACT FROM PUBLISHER]

In this paper, we investigate the effect of anisotropic and correlated non-identical distributions of feature points’ gray level on pose estimation in stereo vision system. The generalized orthogonal iteration (GOI) algorithm for pose estimation with uncertainty-weighted measuring error of feature target is proposed. In this method, the inverse covariance matrix is applied to describe the uncertainty of feature points, and weighted contribution of uncertainty to the error objective function is analysed. By transforming the uncertainty into the covariance-weighted data space, a novel objective function based on spatial collinear error is constructed. The orthogonal iterative algorithm is extended to stereo vision system for pose estimation and the GOI algorithm is deduced, by which the optimized solution to a novel objective function is given. Finally, simulation and actual experimental results show high accuracy and strong robustness of the proposed approach, and should therefore, have potential for a variety of engineering applications. [ABSTRACT FROM PUBLISHER]

We propose a new family of subgradient- and gradient-based methods which converges with optimal complexity for convex optimization problems whose feasible region is simple enough. This includes cases where the objective function is non-smooth, smooth, have composite/saddle structure, or are given by an inexact oracle model. We unified the way of constructing the subproblems which are necessary to be solved at each iteration of these methods. This permitted us to analyse the convergence of these methods in a unified way compared to previous results which required different approaches for each method/algorithm. Our contribution rely on two well-known methods in non-smooth convex optimization: the mirror-descent method (MDM) by Nemirovski-Yudin and the dual-averaging method by Nesterov. Therefore, our family of methods includes them and many other methods as particular cases. For instance, the proposed family of classical gradient methods and its accelerations generalize Devolder et al.'s, Nesterov's primal/dual gradient methods, and Tseng's accelerated proximal gradient methods. Also our family of methods can partially become special cases of other universal methods, too. As an additional contribution, the novel extended MDM removes the compactness assumption of the feasible region and the fixation of the total number of iterations which is required by the original MDM in order to attain the optimal complexity. [ABSTRACT FROM AUTHOR]

This study presents a new trust-region algorithm to solve the -minimization problem with applications to compressed sensing (CS) and image deblurring that will be augmented with a shrinkage operation to produce a new iteration whenever an approximated solution of the trust-region subproblem lies within one and iterate is successful, simultaneously. Otherwise, a nonmonotone Armijo-type line search strategy incorporates with shrinkage technique, which includes a convex combination of the maximum function value of some preceding iterates and the current function value. Therefore, the proposed approach takes advantages of both the effective trust-region and nonmonotone Armijo-type line search with a shrinkage operation. It is believed that selecting an appropriate shrinkage parameter according to a new procedure can improve the efficiency of our algorithm. The global convergence and the R-linear convergence rate of the proposed approach are proved for which numerical results are also reported. [ABSTRACT FROM AUTHOR]

In this article, a recently introduced iterative method based on Green's functions and fixed-point iteration schemes is presented for the approximate solutions of delay and functional differential equations. The approach is especially suited for handling boundary value problems (BVPs). The algorithm is illustrated through a number of examples that confirm the high accuracy and efficiency of the strategy. The results of the test examples show excellent agreement with exact solutions and outperforms other existing numerical iterative schemes. [ABSTRACT FROM AUTHOR]

The study was conducted with the aim to find out random variational-like inclusion involving relaxed monotone, random operators in Hilbert space and construct a new iterative algorithm. The study also proves the existence of random solution of random variational-like inclusion problem and convergence of random iterative sequences generated by random iterative algorithm. The results in this paper unify, improve and extend some well-known results from the literature. [ABSTRACT FROM AUTHOR]

The link constrained Steiner tree problem is a variant of the classic Steiner tree problem where the number of links to be activated must not exceed a pre-fixed value. We introduce a multi-start heuristic to obtain a quick feasible solution. The proposed heuristic is embedded into a decomposition framework based on Lagrangean relaxation. In particular, the relaxed problem is decomposed into two polynomially solvable subproblems and, to tackle the Lagrangean dual, we introduce a dual ascent procedure where just one multiplier at a time is updated. Our approach can be classified as a Lagrangean heuristic. In fact, at each iteration of the dual ascent procedure, the information derived from the solution of the relaxed problem is used to provide a feasible solution, by solving a restricted problem defined on an appropriate subgraph. Several versions of the proposed approach are defined and tested on instances drawn from the scientific literature. [ABSTRACT FROM AUTHOR]

A canard explosion is the dramatic change of period and amplitude of a limit cycle of a system of nonlinear ODEs in a very narrow interval of the bifurcation parameter. It occurs in slow–fast systems and is well understood in singular perturbation problems where a small parameter epsilon defines the time-scale separation. We present an iterative algorithm for the determination of the canard explosion point which can be applied for a general slow–fast system without an explicit small parameter. We also present assumptions under which the algorithm gives accurate estimates of the canard explosion point. Finally, we apply the algorithm to the van der Pol equations, a Templator model for a self-replicating system and a model for intracellular calcium oscillations with no explicit small parameters and obtain very good agreement with results from numerical simulations. [ABSTRACT FROM PUBLISHER]

In this article, we deal with an iteration method for approximating a fixed point of a contraction mapping using Mann’s algorithm under functional random errors. We first show its almost complete convergence to the fixed point by mean of an exponential inequality and then we specify the induced rate of convergence. We finally build a confidence domain for the fixed point. Moreover, some numerical examples are considered. [ABSTRACT FROM AUTHOR]

We present an efficient algorithm for finding the shortest path joining two points in a sequence of triangles in three-dimensional space without planar unfolding. The concept of a funnel associated with a common edge along a sequence of triangles is introduced, that is similar to Lee and Preparata's one in a simple polygon. The sequence of funnels associated with all commonedges of the sequence is constructed and then the shortest path is determined by cusps of these funnels. Such funnels are determined iteratively to their associated edges by the Method of Orienting Curves, which was introduced by Phu [Ein konstruktives Lösungsverfahren für das Problem des Inpolygons kleinsten Umfangs von J. Steiner. Optimization. 1987;18:349-359]. The method consists of the concepts of final curves and orienting curves (the special cases of straightest geodesics). We then show that the shortest path from the cusp of a given funnel to the direct destination in the processed region of the funnel is determined by parts of orienting curves and a final curve. A numerical example for finding the shortest path joining two points in the sequence of triangles is presented and visualized by JavaView software. [ABSTRACT FROM AUTHOR]

It is commonly asserted that the Gibbs sampler is a special case of the Metropolis–Hastings (MH) algorithm. While this statement is true for certain Gibbs samplers, it is not true in general for the version that is taught and used most often, namely, the deterministic scan Gibbs sampler. In this note, I prove that that there exist deterministic scan Gibbs samplers that do not exhibit detailed balance and hence cannot be considered MH samplers. The nuances of various Gibbs sampling schemes are discussed. [ABSTRACT FROM AUTHOR]

We present and explore the behaviour of a branch-and-bound algorithm for calculating valid bounds on thekth largest eigenvalue of a symmetric interval matrix. Branching on the interval elements of the matrix takes place in conjunction with the application of Rohn's method (an interval extension of Weyl's theorem) in order to obtain valid outer bounds on the eigenvalues. Inner bounds are obtained with the use of two local search methods. The algorithm has the theoretical property that it provides bounds to any arbitrary precision(assuming infinite precision arithmetic) within finite time. In contrast with existing methods, bounds for each individual eigenvalue can be obtained even if its range overlaps with the ranges of other eigenvalues. Performance analysis is carried out through nine examples. In the first example, a comparison of the efficiency of the two local search methods is reported using 4000 randomly generated matrices. The eigenvalue bounding algorithm is then applied to five randomly generated matrices with overlapping eigenvalue ranges. Valid and sharp bounds are indeed identified given a sufficient number of iterations. Furthermore, most of the range reduction takes place in the first few steps of the algorithm so that significant benefits can be derived without full convergence. Finally, in the last three examples, the potential of the algorithm for use in algorithms to identify index-1 saddle points of nonlinear functions is demonstrated. [ABSTRACT FROM AUTHOR]

Vibrational spectra and wavefunctions of polyatomic molecules can be calculated at low memory cost using low-rank sum-of-product (SOP) decompositions to represent basis functions generated using an iterative eigensolver. Using a SOP tensor format does not determine the iterative eigensolver. The choice of the interative eigensolver is limited by the need to restrict the rank of the SOP basis functions at every stage of the calculation. We have adapted, implemented and compared different reduced-rank algorithms based on standard iterative methods (block-Davidson algorithm, Chebyshev iteration) to calculate vibrational energy levels and wavefunctions of the 12-dimensional acetonitrile molecule. The effect of using low-rank SOP basis functions on the different methods is analysed and the numerical results are compared with those obtained with the reduced rank block power method. Relative merits of the different algorithms are presented, showing that the advantage of using a more sophisticated method, although mitigated by the use of reduced-rank SOP functions, is noticeable in terms of CPU time. [ABSTRACT FROM AUTHOR]