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modulus-based matrix splitting algorithms for the quasi-complementarity problems

APPLIED NUMERICAL MATHEMATICS 2018年 132卷 127-137页

作者： Wu, Shi-Liang Guo, Peng Anyang Normal Univ Sch Math & Stat Anyang 455000 Peoples R China

In this paper, a class of modulus-based matrix splitting iteration methods for the quasi-complementarity problems is presented. The convergence analysis of the proposed methods is discussed. Numerical experiments show... 详细信息

关键词： Quasi-complementarity problem modulus-based matrix splitting Iteration method Convergence

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modulus-based matrix splitting iteration methods for a class of implicit complementarity problems

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NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS 2016年第4期23卷 629-641页

作者： Hong, Jun-Tao Li, Chen-Liang Guilin Univ Elect Technol Sch Math & Comp Sci Guangxi Coll & Univ Key Lab Data Anal & Computat Guilin 541004 Guangxi Peoples R China

Some modulus-based matrix splitting iteration methods for a class of implicit complementarity problem are presented, and their convergence analysis is given. Numerical experiments confirm the theoretical analysis and ... 详细信息

关键词： implicit complementarity problem modulus-based matrix splitting iterative method convergence

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The selection of the optimal parameter in the modulus-based matrix splitting algorithm for linear complementarity problems

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COMPUTATIONAL OPTIMIZATION AND APPLICATIONS 2021年第2期80卷 617-638页

作者： Li, Zhizhi Zhang, Huai Ou-Yang, Le Shenzhen Univ Coll Elect & Informat Engn Guangdong Key Lab Intelligent Informat Proc Shenzhen 518060 Peoples R China Shenzhen Univ Coll Elect & Informat Engn Shenzhen Key Lab Media Secur Shenzhen 518060 Peoples R China Univ Chinese Acad Sci Key Lab Computat Geodynam Beijing 100049 Peoples R China Shenzhen Inst Artificial Intelligence & Robot Soc Shenzhen 518060 Peoples R China

The modulus-based matrix splitting (MMS) algorithm is effective to solve linear complementarity problems (Bai in Numer Linear Algebra Appl 17: 917-933, 2010). This algorithm is parameter dependent, and previous studies mainly focus on giving the convergence interval of the iteration parameter. Yet the specific selection approach of the optimal parameter has not been systematically studied due to the nonlinearity of the algorithm. In this work, we first propose a novel and simple strategy for obtaining the optimal parameter of the MMS algorithm by merely solving two quadratic equations in each iteration. Further, we figure out the interval of optimal parameter which is iteration independent and give a practical choice of optimal parameter to avoid iteration-based computations. Compared with the experimental optimal parameter, the numerical results from three problems, including the Signorini problem of the Laplacian, show the feasibility, effectiveness and efficiency of the proposed strategy.

关键词： Optimal parameter Practical solution Quadratic equation modulus-based matrix splitting Linear complementarity problems

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A variant of two-step modulus-based matrix splitting iteration method for Retinex problem

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COMPUTATIONAL & APPLIED MATHEMATICS 2022年第6期41卷 1-13页

作者： Chen, Fang Zhu, Yu Beijing Informat Sci & Technol Univ Sch Appl Sci Beijing 100192 Peoples R China

based on a variational optimization model, and by imposing physical constraints on the reflection value, and deriving deformation of the Retinex problem, we find that the Retinex problem is equivalent to a linear complementarity problem and its solution can be computed by solving an equivalent fixed-point equation. In light of the theoretical analysis of the special structure of the system matrix of the linear complementarity problem, we propose a variant of the two-step modulus-based matrix splitting iteration method, and then prove its unconditional convergence. We further give practically quasi-optimal values of the involved iteration parameters in this method. The numerical results show that the variant of the two-step modulus-based matrix splitting iteration method is effective in terms of iteration steps, computing time, and natural image quality evaluator.

关键词： Linear complementarity problem Two-step iteration method modulus-based matrix splitting Retinex problem

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The convergence of a modulus-based matrix splitting iteration method for solving the implicit complementarity problems

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JOURNAL OF APPLIED MATHEMATICS AND COMPUTING 2023年第1期69卷 853-870页

作者： Fang, Ximing Zhaoqing Univ Sch Math & Stat Zhaoqing 526000 Peoples R China

In this paper, we discuss a modulus-based matrix splitting iteration method for solving the implicit complementarity problems and propose the convergence conditions from the spectral radius and matrix norm. The numeri... 详细信息

关键词： Implicit complementarity problem modulus-based matrix splitting Convergence

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The Nonlinear Lopsided HSS-Like modulus-based matrix splitting Iteration Method for Linear Complementarity Problems with Positive-Definite Matrices

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Communications on Applied Mathematics and Computation 2021年第1期3卷 109-122页

作者： Lu Jia Xiang Wang Xiao-Yong Xiao Department of Mathematics Nanchang UniversityNanchang 330031China Numerical Simulation and High-Performance Computing Laboratory Nanchang UniversityNanchang 330031China

In this paper,by means of constructing the linear complementarity problems into the corresponding absolute value equation,we raise an iteration method,called as the nonlinear lopsided HSS-like modulus-based matrix splitting iteration method,for solving the linear complementarity problems whose coefficient matrix in R^(n×n)is large sparse and positive *** the convergence analysis,it is appreciable to see that the proposed method will converge to its accurate solution under appropriate *** examples demonstrate that the presented method precede to other methods in practical implementation.

关键词： Linear complementarity problem modulus-based matrix splitting Lopsided HSS

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A class of modulus-based matrix splitting methods for vertical linear complementarity problem

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OPTIMIZATION 2023年第10期72卷 2499-2516页

作者： Li, Cui-Xia Wu, Shi-Liang Yunnan Normal Univ Sch Math Kunming Yunnan Peoples R China

In this paper, by transforming the vertical linear complementarity problem (VLCP) as a certain absolute value equation, we design a class of modulus-based matrix splitting iteration methods for solving the VLCP. The convergence properties of the proposed methods are discussed in depth. By making use of some numerical experiments, we confirm the efficiency of the proposed methods. Numerical results show that the proposed methods are superior to the classical modulus-based matrix splitting iteration methods.

关键词： Vertical linear complementarity problem modulus-based matrix splitting iteration method convergence

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Two Variants of Robust Two-Step modulus-based matrix splitting Iteration Methods for Mixed-Cell-Height Circuit Legalization Problem

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COMMUNICATIONS ON APPLIED MATHEMATICS AND COMPUTATION 2024年 1-22页

作者： Wang, Lu-Xin Cao, Yang Shen, Qin-Qin Nantong Univ Sch Informat Sci & Technol Nantong 226019 Jiangsu Peoples R China Jiangsu Shipping Coll Dept Basic Teaching Nantong 226010 Jiangsu Peoples R China Nantong Univ Sch Transportat & Civil Engn Nantong 226019 Jiangsu Peoples R China

The mathematical formulation of the mixed-cell-height circuit legalization (MCHCL) problem can be expressed by a linear complementarity problem (LCP) with the system matrix being a block two-by-two saddle point matrix. based on the robust modulus-based matrix splitting (RMMS) iteration method and its two-step improvement (RTMMS) studied recently, the well-known Hermitian and skew-Hermitian splitting iteration method and the generalized successive overrelaxation iteration method for solving saddle point linear systems, two variants of robust two-step modulus-based matrix splitting (VRTMMS) iteration methods are proposed for solving the MCHCL problem. Convergence analyses of the proposed two iteration methods are studied in detail. Finally, five test problems are presented. Numerical results show that the proposed two VRTMMS iteration methods not only take full use of the sparse property of the circuit system but also speed up the computational efficiency of the existing RMMS and RTMMS iteration methods for solving the MCHCL problem.

关键词： Mixed-cell-height circuit legalization (MCHCL) Linear complementarity problem (LCP) modulus-based method modulus-based matrix splitting Convergence

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A Two-Step modulus-based matrix splitting Iteration Method Without Auxiliary Variables for Solving Vertical Linear Complementarity Problems

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Communications on Applied Mathematics and Computation 2024年第4期6卷 2475-2492页

作者： Hua Zheng Xiaoping Lu Seakweng Vong School of Mathematics and Statistics Shaoguan UniversityShaoguan 512005GuangdongChina School of Computer Science and Engineering Macao University of Science and TechnologyMacaoChina Department of Mathematics University of MacaoMacaoChina

In this paper,a two-step iteration method is established which can be viewed as a generalization of the existing modulus-based methods for vertical linear complementarity problems given by He and Vong(***.134:108344,2022).The convergence analysis of the proposed method is established,which can improve the existing *** examples show that the proposed method is efficient with the two-step technique.

关键词： Vertical linear complementarity problem modulus-based matrix splitting Two-step metho

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On estimation of the optimal parameter of the modulus-based matrix splitting algorithm for linear complementarity problems on second-order cones

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NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS 2023年第4期30卷 e2480-e2480页

作者： Li, Zhizhi Zhang, Huai Univ Chinese Acad Sci Key Lab Computat Geodynam Beijing Peoples R China Qingdao Natl Lab Marine Sci & Technol Lab Marine Mineral Resources Qingdao Peoples R China Univ Chinese Acad Sci Key Lab Computat Geodynam Beijing 100049 Peoples R China

There are many studies on the well-known modulus-based matrix splitting (MMS) algorithm for solving complementarity problems, but very few studies on its optimal parameter, which is of theoretical and practical importance. Therefore and here, by introducing a novel mapping to explicitly cast the implicit fixed point equation and thus obtain the iteration matrix involved, we first present the estimation approach of the optimal parameter of each step of the MMS algorithm for solving linear complementarity problems on the direct product of second-order cones (SOCLCPs). It also works on single second-order cone and the non-negative orthant. On this basis, we further propose an iteration-independent optimal parameter selection strategy for practical usage. Finally, the practicability and effectiveness of the new proposal are verified by comparing with the experimental optimal parameter and the diagonal part of system matrix. In addition, with the optimal parameter, the effectiveness of the MMS algorithm can indeed be greatly improved, even better than the state-of-the-art solvers SCS and SuperSCS that solve the equivalent SOC programming.

关键词： iteration-independent linear complementarity problems modulus-based matrix splitting optimal parameter second-order cone

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