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We consider the problem of tensor (i.e., multidimensional array) inpainting in this paper. By using higher-order singular value decomposition, we propose an iterative algorithm that performs soft thresholding on entries of the core tensor and then reconstructs via the directional orthogonal matrices. An inpainted tensor is obtained at the end of the iteration. Simulations conducted over color images, video frames, and MR images validate that the proposed algorithm is competitive with state-of-the-art completion algorithms. The evaluation is made in terms of quality metrics and visual comparison. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to investigate the effect of individual arcs and nodes on the description of feasibility in an uncapacitated network. This is done by developing an iterative algorithm for finding all (necessary) Gale--Hoffman inequalities for the network. [ABSTRACT FROM AUTHOR]

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]

In this paper, we introduce and analyze a new hybrid extragradient-like iterative algorithm for finding a common solution of a generalized mixed equilibrium problem, a system of generalized equilibrium problems and a fixed point problem of infinitely many non expansive mappings. Under some mild conditions, we prove the strong convergence of the sequence generated by the proposed algorithm to a common solution of these three problems. Such solution also solves an optimization problem. Several special cases are also discussed. The results presented in this paper are the supplement, extension, improvement and generalization of the previously known results in this area. [ABSTRACT FROM AUTHOR]

This paper describes a new direct search method for solving non-standard constrained optimization problems for which standard methodologies do not work properly. Our method (the Rational Iterative Multisection-RIM-algorithm) consists of different stages that can be interpreted as solutions according to different precision requirements. We have performed an application of RIM method to the case of public inputs provision. We prove that the RIM approach and standard methodologies achieve the same results with regular optimization problems while the RIM algorithm takes advantage over others comparable direct-search methods when facing non-standard optimization problems. [ABSTRACT FROM AUTHOR]

This paper describes a numerical procedure for solving two-dimensional elastostatics problems with multiple circular holes and elastic inclusions in a finite domain with a circular boundary. The inclusions may have arbitrary elastic properties, different from those of the matrix, and the holes may be traction free or loaded with uniform normal pressure. The loading can be applied on all or part of the finite external boundary. Complex potentials are expressed in the form of integrals of the tractions and displacements on the boundaries. The unknown boundary tractions and displacements are approximated by truncated complex Fourier series. A linear algebraic system is obtained by using Taylor series expansion without boundary discretization. The matrix of the linear system has diagonal submatrices on its diagonal, which allows the system to be effectively solved by using a block Gauss-Seidel iterative algorithm. [ABSTRACT FROM AUTHOR]

Loop tiling and unrolling are two important program transformations to exploit locality and expose instruction level parallelism, respectively. However, these transformations are not independent and each can adversely affect the goal of the other. Furthermore, the best combination will vary dramatically from one processor to the next. In this paper, we therefore address the problem of how to select tile sizes and unroll factors simultaneously. We approach this problem in an architecturally adaptive manner by means of iterative compilation, where we generate many versions of a program and decide upon the best by actually executing them and measuring their execution time. We evaluate several iterative strategies based on genetic algorithms, random sampling and simulated annealing. We compare the levels of optimization obtained by iterative compilation to several well-known static techniques and show that we outperform each of them on a range of benchmarks across a variety of architectures. Finally, we show how to quantitatively trade-off the number of profiles needed and the level of optimization that can be reached. In this way, we can reach high levels of optimization within 50 iterations. [ABSTRACT FROM AUTHOR]

In this paper, we propose a new iterative algorithm to approximate fixed points of total asymptotically nonexpansive mappings in $\operatorname{CAT}(0)$ spaces. We also provide two examples to illustrate the convergence behavior of the proposed algorithm and numerically compare the convergence of the proposed iteration scheme with the existing schemes. [ABSTRACT FROM AUTHOR]

This paper provides a policy iteration algorithm for solving communicating Markov decision processes (MDPs) with average reward criterion. The algorithm is based on the result that for communicating MDPs there is an optimal policy which is unichain. The improvement step is modified to select only unichain policies; consequently the nested optimality equations of Howard's multichain policy iteration algorithm are avoided. Properties and advantages of the algorithm are discussed and it is incorporated into a decomposition algorithm for solving multichain MDPs. Since it is easier to show that a problem is communicating than unichain we recommend use of this algorithm instead of unichain policy iteration. [ABSTRACT FROM AUTHOR]

In this paper, the infinite horizon Markovian decision programming with recursive reward functions is discussed. We show that Bellman's optimal principle is applicable for our model. Then, a sufficient and necessary condition for a policy to be optimal is given. For the stationary case, an iteration algorithm for finding a stationary optimal policy is designed. The algorithm is a generalization of Howard's [7] and Iwamoto's [3] algorithms. [ABSTRACT FROM AUTHOR]

The parallel quasi-Newton method based on updating conjugate subspaces proposed in [4] can be very effective for large-scale sparse minimization because conjugate subspaces with respect to sparse Hessians are usually easy to obtain. We demonstrate this point in this paper for the partially separable case with matrices updated by a quasi-Newton scheme of GRIEWANK and TOINT [2,3]. The algorithm presented is suitable for parallel computation and economical in computer storage. Some testing results of the algorithm on an Alliant FX/8 minisupercomputer are reported. [ABSTRACT FROM AUTHOR]

Fast multipole boundary element methods (FMBEMs) are developed based on the couple of fast multipole algorithm and generalized minimal residual algorithm. The FMBEMs improve the efficiency of conventional BEMs, accelerate the computing, enlarge the solving scale, and it is applied in various engineering fields. The paper tried to do a brief review for the FMBEMs, and focus on the description of basic principles and applications in rolling engineering. The basic principles and main frameworks of two typical methods of FMBEMs (sphere harmonic function multipole BEM and Taylor series multipole BEM) are briefly described, and then the key numerical iterative and preconditioning techniques suitable for the FMBEMs are introduced. The typical numerical examples are presented, including the elasticity problems, the elastic contact problems and the elastoplasticity problems, etc. The validity and effectiveness of FMBEMs are effectively illustrated by engineering analysis examples. The numerical results suggest that the FMBEMs are suitable for the analysis and solution of large scale rolling engineering problems. The implementation process of numerical analysis can provide useful reference for the applications in other engineering fields. [ABSTRACT FROM AUTHOR]

Solving large sparse linear systems is essential in numerous scientific domains. Several algorithms, based on direct or iterative methods, have been developed for parallel architectures. On distributed grids consisting of processors located in distant geographical sites, their performance may be unsatisfactory because they suffer from too many synchronizations and communications. The GREMLINS code has been developed for solving large sparse linear systems on distributed grids. It implements the multisplitting method that consists in splitting the original linear system into several subsystems that can be solved independently. In this paper, the performance of the GREMLINS code obtained with several libraries for solving the linear subsystems is analyzed. Its performance is also compared with that of the widely used PETSc library that enables one to develop portable parallel applications. Numerical experiments have been carried out both on local clusters and on distributed grids. [ABSTRACT FROM AUTHOR]

This paper is concerned with the numerical treatment of inverse heat conduction problems. In particular, we combine recent results on the regularization of ill-posed problems by iterated soft shrinkage with adaptive wavelet algorithms for the forward problem. The analysis is applied to an inverse parabolic problem that stems from the industrial process of melting iron ore in a steel furnace. Some numerical experiments that confirm the applicability of our approach are presented. [ABSTRACT FROM AUTHOR]

The construction of the iteration procedure for synthesizing the law of control of observation over the processes, appeared one after another according to random flux regularities, is considered. The general approach to solution of the problem and the approximate algorithm for synthesizing the law of observations control are given for the case of a simple Poissonian flux. The example is presented in the paper. [ABSTRACT FROM AUTHOR]

In location-routing problems, the objective is to locate one or many depots within a set of sites (representing customer locations or cities) and to construct delivery routes from the selected depot or depots to the remaining sites at least system cost. The objective function is the sum of depot operating costs, vehicle acquisition costs and routing costs. This paper considers one such problem m which a weight is assigned to each site and where sites are to be visited by vehicles having a given capacity. The solution must be such that the sum of the weights of sites visited on any given route does not exceed the capacity of the visiting vehicle. The formulation of an integer linear program for this problem involves degree constraints generalized subtour elimination constraints, and chain baring constraints. An exact algorithm, using initial relaxation of most of the problem constraints, is presented which is capable of solving problems with up to twenty sites within a reasonable number of iterations [ABSTRACT FROM AUTHOR]

In this paper, we propose two iterative methods for finding a common solution of a finite family of equilibrium problems for pseudomonotone bifunctions. The first is a parallel hybrid extragradientcutting algorithm which is extended from the previously known one for variational inequalities to equilibrium problems. The second is a new cyclic hybrid extragradient-cutting algorithm. In the cyclic algorithm, using the known techniques, we can perform and develop practical numerical experiments. [ABSTRACT FROM AUTHOR]

In this paper, an efficient algorithm is established for computing the maximum (minimum) angular separation ρ( ρ), the corresponding apparent position angles ( $\theta|_{\rho_{\rm max}}$, $\theta|_{\rho_{\rm min}}$) and the individual masses of visual binary systems. The algorithm uses Reed's formulae (1984) for the masses, and a technique of one-dimensional unconstrained minimization, together with the solution of Kepler's equation for $(\rho_{\rm max}, \theta|_{\rho_{\rm max}})$ and $(\rho_{\rm min}, \theta|_{\rho_{\rm min}})$. Iterative schemes of quadratic coverage up to any positive integer order are developed for the solution of Kepler's equation. A sample of 110 systems is selected from the Sixth Catalog of Orbits (Hartkopf et al.). Numerical studies are included and some important results are as follows: (1) there is no dependence between ρ and the spectral type and (2) a minor modification of Giannuzzi's () formula for the upper limits of ρ functions of spectral type of the primary. [ABSTRACT FROM AUTHOR]

The solution of 3 D elastic-plastic frictional contact problems belongs to the unspecified boundary problems where the interaction between two kinds of nonlinearities should occur. Considering the difficulties for the solution of 3D frictional contact problems, the key part is the determination of the tangential slip states at the contact points, and a great amount of computing work is needed for a high accuracy result. A new method based on a combination of programming and iteration methods, which are respectively known as two main kinds of methods for contact analysis, was put forward to deal with 3D elastic-plastic contact problems. Numerical results demonstrate the efficiency of the algorithm illustrated here. [ABSTRACT FROM AUTHOR]

We investigate an inverse problem of identifying a Robin coefficient with a sparse structure in the Laplace equation from noisy boundary measurements. The sparse structure of the Robin coefficient γ is understood as a small perturbation of a reference profile γ in the sense that their difference γ− γ has a small support. This problem is formulated as an optimal control problem with an L-regularization term. An iteratively reweighted least-squares algorithm with an inner semismooth Newton iteration is employed to solve the resulting optimization problem, and the convergence of the iteratively weighted least-squares algorithm is established. Numerical results for two-dimensional problems are presented to illustrate the efficiency of the proposed method. [ABSTRACT FROM AUTHOR]

New versions and extensions of Benson's outer approximation algorithm for solving linear vector optimization problems are presented. Primal and dual variants are provided in which only one scalar linear program has to be solved in each iteration rather than two or three as in previous versions. Extensions are given to problems with arbitrary pointed solid polyhedral ordering cones. Numerical examples are provided, one of them involving a new set-valued risk measure for multivariate positions. [ABSTRACT FROM AUTHOR]

We consider a problem of solution of a multi-valued inclusion on a cone segment. In the case where the underlying mapping possesses Z type properties we suggest an extension of Gauss-Seidel algorithms from nonlinear equations. We prove convergence of a modified double iteration process under rather mild additional assumptions. Some results of numerical experiments are also presented. [ABSTRACT FROM AUTHOR]

Based on the ideas of infeasible interior-point methods and predictor-corrector algorithms, two interior-point predictor-corrector algorithms for the second-order cone programming (SOCP) are presented. The two algorithms use the Newton direction and the Euler direction as the predictor directions, respectively. The corrector directions belong to the category of the Alizadeh-Haeberly-Overton (AHO) directions. These algorithms are suitable to the cases of feasible and infeasible interior iterative points. A simpler neighborhood of the central path for the SOCP is proposed, which is the pivotal difference from other interior-point predictor-corrector algorithms. Under some assumptions, the algorithms possess the global, linear, and quadratic convergence. The complexity bound O( rln( ɛ/ ɛ)) is obtained, where r denotes the number of the second-order cones in the SOCP problem. The numerical results show that the proposed algorithms are effective. [ABSTRACT FROM AUTHOR]

This article presents an algorithm that performs a decentralized detection of the global convergence of parallel asynchronous iterative applications. This algorithm is fault tolerant. It runs a decentralized saving procedure which enables this algorithm, after a node’s crash, to replace the dead node by a new one which will continue the computing task from the last check point. Combined with the advantages of the asynchronous iteration model, this method allows us to compute very large scale problems using highly volatile parallel architectures like Peer-to-Peer and distributed clusters architectures. We also present the implementation of this algorithm in the JaceP2P platform which is dedicated to designing and executing parallel asynchronous iterative applications in volatile environments. Numerous experiments show the robustness and the efficiency of our algorithm. [ABSTRACT FROM AUTHOR]

This work deals with the convergence acceleration of iterative nonlinear methods. Two convergence accelerating techniques are evaluated: the Modified Mininal Polynomial Extrapolation Method (MMPE) and the Padé approximants. The algorithms studied in this work are iterative correctors: Newton’s modified method, a high-order iterative corrector presented in Damil et al. (Commun Numer Methods Eng 15:701–708, 1999) and an original algorithm for vibration of viscoelastic structures. We first describe the iterative algorithms for the considered nonlinear problems. Secondly, the two accelerating techniques are presented. Finally, through several numerical tests from the thin shell theory, Navier–Stokes equations and vibration of viscoelastic shells, the advantages and drawbacks of each accelerating technique is discussed. [ABSTRACT FROM AUTHOR]

The multivalued general mixed implicit equilibrium-like problems are introduced and studied. To solve these problems, a new predictor-corrector iterative algorithm is proposed and analyzed using the auxiliary principle technique. The convergence of the suggested algorithm is also proved in weaker conditions. [ABSTRACT FROM AUTHOR]

The article presents information on a new methodology for correcting the signal cumulative phenomenon in injection rate measurements. It is used to enhance the signal treatment algorithm and it depends on controlling the signal of the injection measurements through appropriate numerical solutions and iterative techniques to take out the pressure cumulative phenomenon which influences the injection rate measurement. The method is authenticated by its affirmative outcomes. It is also suggested that the method can be applied to any measurement system with same cumulative phenomenon behaviors.

A thermally driven mushy cell tracking algorithm for phase-change problems with a moving boundary is presented. The equation used to track the moving boundary is based on energy balance over the mushy cell and is applied to advance a moving front in a cell-by-cell manner. The efficacy of the tracking algorithm is demonstrated on specific problems solved using the finite volume method. An implicit scheme is adopted to ensure that the numerical solution is unconditionally stable in time. A preconditioned conjugated gradient (P-CG) solver is implemented to ensure that solutions converge in a finite number of iterations. Four benchmark cases are used to validate the algorithm including solidification in one dimensional space (two-region problem), melting of pure aluminum in two-dimensional (2D) space, solidification with periodic boundary conditions, and solidification of one-region problem. The results obtained show that the current algorithm is capable of converging to accurate solutions for moving fronts and the numerical predications are in excellent agreement with corresponding analytical solutions. [ABSTRACT FROM AUTHOR]

A robust analog of the Nadaraya-Watson regression estimate is considered. A solution is obtained in the class of censor algorithms. A criterion and iteration procedure for determining a censored sample are proposed. The criterion is based on the analysis of residuals (errors) of estimation. [ABSTRACT FROM AUTHOR]

The article proposes and examines an iterative algorithm for a finite family of non-expansive mappings T1, T2, …, Tr. The study uses various iterative schemes to examine a common fixed point of a finite family of non-expansive mappings under some type of control conditions. It reveals that the proposed iterative algorithm converges strongly to a common fixed point of T1, T2, …, Tr. The section also provides computations of the problem and explains how they arrived to their conclusion.

We investigate the questions of existence of positive solution for the nonlocal problem -M(∥u∥²)Δu = f (λ,u) in Ω and u = 0 on ∂Ω, where Ω is a bounded smooth domain of ℝN, and M and f are continuous functions. [ABSTRACT FROM AUTHOR]

The special constraint structure and large dimension are characteristic for multistage stochastic optimization. This results from modeling future uncertainty via branching process or scenario tree. Most efficient algorithms for solving this type of problems use certain decomposition schemes, and often only a part of the whole set of scenarios is taken into account in order to make the problem tractable. We propose a primal-dual method based on constraint aggregation, which constructs a sequence of iterates converging to a solution of the initial problem. At each iteration, however, only a reduced sub-problem with smaller number of aggregate constraints has to be solved. Number of aggregates and their composition are determined by the user, and the procedure for calculating aggregates can be parallelized. The method provides a posteriori estimates of the quality of the current solution approximation in terms of the objective function value and the residual. [ABSTRACT FROM AUTHOR]

We develop an iterative algorithm based on right-hand side decomposition for the solution of multicommodity network flow problems. At each step of the proposed iterative procedure the coupling constraints are eliminated by subdividing the shared capacity resource among the different commodities and a master problem is constructed which attempts to improve sharing of the resources at each iteration. As the objective function of the master problem is nonsmooth, we apply to it a new optimization technique which does not require the exact solutions of the single commodity flow subproblems. This technique is based on the notion of ∈- subgradients instead of subgradients and is suitable for parallel implementation. Extensions to the nonlinear, convex separable case are also discussed. [ABSTRACT FROM AUTHOR]