Linearized Methods for Tensor Complementarity Problems
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DOI: 10.1007/s10957-019-01627-3
Abstract: In this paper, we first propose a linearized method for solving the tensor complementarity problem. The subproblems of the method can be solved by solving linear complementarity problems with a constant matrix. We show that… read more here.
Keywords: complementarity problems; tensor complementarity; linearized methods; complementarity ... See more keywords
A smoothing Levenberg-Marquardt method for nonlinear complementarity problems
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DOI: 10.1007/s11075-018-0485-3
Abstract: As is well-known, Jacobian smoothing method is a popular one to solve nonlinear complementarity problems, in which the Jacobian consistency is stressed. By investigating an element of related functions’ B-differential, a smoothing Levenberg-Marquardt(LM) method is… read more here.
Keywords: levenberg marquardt; complementarity problems; nonlinear complementarity; marquardt method ... See more keywords
Note on error bounds for linear complementarity problems of Nekrasov matrices
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DOI: 10.1007/s11075-019-00685-y
Abstract: García-Esnaola and Peña (Numer. Algor. 67 , 655–667, 2014 ) presented an error bound involving a parameter for linear complementarity problems of Nekrasov matrices. This bound is not effective in some cases because it tends… read more here.
Keywords: linear complementarity; complementarity problems; error; problems nekrasov ... See more keywords
A two-step modulus-based matrix splitting iteration method for horizontal linear complementarity problems
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DOI: 10.1007/s11075-020-00954-1
Abstract: In this paper, for solving horizontal linear complementarity problems, a two-step modulus-based matrix splitting iteration method is established. The convergence analysis of the proposed method is presented, including the case of accelerated overrelaxation splitting. Numerical… read more here.
Keywords: linear complementarity; complementarity problems; step modulus; two step ... See more keywords
Column sufficient tensors and tensor complementarity problems
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DOI: 10.1007/s11464-018-0681-4
Abstract: Stimulated by the study of sufficient matrices in linear complementarity problems, we study column sufficient tensors and tensor complementarity problems. Column sufficient tensors constitute a wide range of tensors that include positive semi-definite tensors as… read more here.
Keywords: column sufficient; sufficient tensors; complementarity problems; tensor complementarity ... See more keywords
The sparsest solutions to Z-tensor complementarity problems
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DOI: 10.1007/s11590-016-1013-9
Abstract: Finding the sparsest solutions to a tensor complementarity problem is generally NP-hard due to the nonconvexity and noncontinuity of the involved $$\ell _0$$ℓ0 norm. In this paper, a special type of tensor complementarity problems with… read more here.
Keywords: complementarity problems; solutions tensor; sparsest solutions; tensor complementarity ... See more keywords
Complementarity Problems in Structural Engineering: An Overview
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DOI: 10.1007/s11831-015-9158-8
Abstract: This paper summarizes the formulation of structural engineering problems concerned with inelastic phenomena that can be described in complementarity format. This mathematical construct can be transferred to the discretized version of the continuum problem by… read more here.
Keywords: engineering; complementarity problems; engineering overview; problems structural ... See more keywords
The relaxation modulus-based matrix splitting iteration methods for circular cone nonlinear complementarity problems
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DOI: 10.1007/s40314-018-0687-2
Abstract: In this paper, we study a class of nonlinear complementarity problems associated with circular cone (CCNCP for short), which is a type of non-symmetric cone complementarity problems. Useful properties of the circular cone are investigated,… read more here.
Keywords: iteration methods; cone; complementarity problems; modulus based ... See more keywords
Iterative complexities of a class of homogeneous algorithms for monotone nonlinear complementarity problems over symmetric cones
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DOI: 10.1080/02331934.2018.1477942
Abstract: ABSTRACT This paper provides an analysis of the iterative complexities of a class of homogeneous algorithms for monotone nonlinear complementarity problems over symmetric cones. The proof of the complexity bounds requires that the nonlinear transformation… read more here.
Keywords: symmetric cones; complementarity problems; homogeneous algorithms; problems symmetric ... See more keywords
Convergence Analysis of a Trust-Region Multidimensional Filter Method for Nonlinear Complementarity Problems
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DOI: 10.1155/2020/2539196
Abstract: For solving nonlinear complementarity problems, a new algorithm is proposed by using multidimensional filter techniques and a trust-region method. The algorithm is shown to be globally convergent under the reasonable assumptions and does not depend… read more here.
Keywords: nonlinear complementarity; complementarity problems; multidimensional filter; trust region ... See more keywords
Convergence analysis of modulus-based matrix splitting iterative methods for implicit complementarity problems
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DOI: 10.1186/s13660-017-1593-7
Abstract: In this paper, we demonstrate a complete version of the convergence theory of the modulus-based matrix splitting iteration methods for solving a class of implicit complementarity problems proposed by Hong and Li (Numer. Linear Algebra… read more here.
Keywords: complementarity problems; matrix splitting; modulus based; matrix ... See more keywords