The modulus-based nonsmooth Newton’s method for solving linear complementarity problems

Zheng, Hua; Li, Wen

doi:10.1016/j.cam.2015.04.006

Cited by 30 publications

(2 citation statements)

References 25 publications

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“…The LCP has been well studied by using its modulus-based reformulation [52][53][54][55], and these studies provide important resources for further research on the TCP.…”

Section: Remark 42mentioning

confidence: 99%

Tensor Complementarity Problems—Part II: Solution Methods

Huang

2019

J Optim Theory Appl

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This work, with its three parts, reviews the state-of-the-art of studies for the tensor complementarity problem and some related models. In the first part of this paper, we have reviewed the theoretical developments of the tensor complementarity problem and related models. In this second part, we review the developments of solution methods for the tensor complementarity problem. It has been shown that the tensor complementarity problem is equivalent to some known optimization problems, or related problems such as systems of tensor equations, systems of nonlinear equations, and nonlinear programming problems, under suitable assumptions. By solving these reformulated problems with the help of structures of the involved tensors, several numerical methods have been proposed so that a solution of the tensor complementarity problem can be found. Moreover, based on a polynomial optimization model, a semidefinite relaxation method is presented so that all solutions of the tensor complementarity problem can be found under the assumption that the solution set of the problem is finite. Further applications of the tensor complementarity problem will be given and discussed in the third part of this paper. KeywordsTensor complementarity problem • System of tensor equations • System of non-smooth equations • Mixed integer programming • Semidefinite relaxation method Mathematics Subject Classification 90C33 • 90C30 • 65H10 B Liqun Qi

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“…The LCP has been well studied by using its modulus-based reformulation [52][53][54][55], and these studies provide important resources for further research on the TCP.…”

Section: Remark 42mentioning

confidence: 99%

Tensor Complementarity Problems—Part II: Solution Methods

Huang

2019

J Optim Theory Appl

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“…Bai [20] presented a unified framework for the construction of modulus-based matrix splitting iteration methods. Since then, many scholars have developed various kinds of modulus-based matrix splitting iteration methods; see, for example, [21][22][23] for LCP and [24,25] for NCP. Recently, Wu and Li [26] proposed a class of new modulusbased matrix splitting methods for LCP.…”

Section: Introductionmentioning

confidence: 99%

An Efficient Class of Modulus-Based Matrix Splitting Methods for Nonlinear Complementarity Problems

Xie

2021

Mathematical Problems in Engineering

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In this paper, we present an efficient method for finding a numerical solution for nonlinear complementarity problems (NCPs). We first reformulate an NCP as an equivalent system of fixed-point equations and then present a modulus-based matrix splitting iteration method. We prove the convergence of the proposed method with theorems with the relevant conditions. Our preliminary numerical results show that the method is feasible and effective.

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The modulus-based nonsmooth Newton’s method for solving a class of nonlinear complementarity problems of P-matrices

Zheng

Vong²

2018

Calcolo

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The modulus-based nonsmooth Newton’s method for solving linear complementarity problems

Cited by 30 publications

References 25 publications

Tensor Complementarity Problems—Part II: Solution Methods

Tensor Complementarity Problems—Part II: Solution Methods

An Efficient Class of Modulus-Based Matrix Splitting Methods for Nonlinear Complementarity Problems

The modulus-based nonsmooth Newton’s method for solving a class of nonlinear complementarity problems of P-matrices

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