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RESTRICTED ADDITIVE SCHWARZ METHOD FOR A KIND OF nonlinear complementarity problem

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Journal of Computational Mathematics 2014年第5期32卷 547-559页

作者： Hongru Xu Kekun Huang Shuilian Xie Zhe Sun School of Mathematics Jiaying University Meizhou 514015 China College of Mathematics and Information Science Jiangxi Normal University Nanchang 330022 China

In this paper, a new Schwarz method called restricted additive Schwarz method （RAS） is presented and analyzed for a kind of nonlinear complementarity problem （NCP）. The method is proved to be convergent by using weighted maximum norm. Besides, the effect of overlap on RAS is also considered. Some preliminary numerical results are reported to compare the performance of RAS and other known methods for NCP.

关键词： nonlinear complementarity problem nonlinear source term Restricted addi-tive Schwarz method Weighted max norm.

Modulus-Based Multisplitting Iteration Method for a Class of Weakly nonlinear complementarity problem

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Communications on Applied Mathematics and Computation 2021年第3期3卷 419-427页

作者： Guangbin Wang Fuping Tan Department of Mathematics Qingdao Agricultural UniversityQingdao 266109Shandong ProvinceChina Department of Mathematics Shanghai UniversityShanghai 200444China

In this paper,we present a modulus-based multisplitting iteration method based on multisplitting of the system matrix for a class of weakly nonlinear complementarity *** we prove the convergence of the method when the... 详细信息

关键词： Modulus-based multisplitting method nonlinear complementarity problem H-matrix

PREDICTOR-CORRECTOR METHOD FOR nonlinear complementarity problem

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Acta Mathematicae Applicatae Sinica 1997年第3期13卷 321-328页

作者：罗智泉吴士泉叶荫宇 CRI McMaster University Hamilton Canada Institute of Applied Mathematics the Chinese Academy of Sciences Beijing China Department of Management Sciences The University of Iowa Iowa City USA

Recently, Ye et al.[2] proved that the predictor-corrector method proposed by Mizuno et al[1] maintains O( L)-iteration complexity while exhibiting the quadratic convergence of the dual gap to zero under very mild conditions. This impressive result becomes the best-known in the interior point methods. In this paper, we modify the predictor-corrector method and then extend it to solving the nonlinear complementarity problem. We prove that the new method has a ( log(1/ε))-iteration complexity while maintaining the quadratic asymptotic convergence.

关键词： Interior point method nonlinear complementarity problem monotone mapping,complexity quadratic convergence

Projection and Contraction Methods for nonlinear complementarity problem

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Wuhan University Journal of Natural Sciences 2000年第4期5卷 391-396页

作者： Zhao She-feng, Fei Pu-sheng College of Mathematics and Computer Science,Wuhan University,Wuhan 430072,China Wuhan University College of Mathematics and Computer Science Wuhan China (GRID:grid.49470.3e) (ISNI:***)

We applied the projection and contraction method to nonlinear complementarity problem (NCP). Moveover, we proposed an inexact implicit method for (NCP) and proved the convergence.

关键词： nonlinear complementarity problem projection and contraction method implicit method

Multiobjective Optimization Method for Solving nonlinear complementarity problem

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Multiobjective Optimization Method for Solving Nonlinear Com...

A NEW SMOOTHING EQUATIONS APPROACH TO THE nonlinear complementarity problemS

2011 Chinese Control and Decision Conference（CCDC）

作者： Longquan Yong Department of Mathematics,Shaanxi University of Technology,Hanzhong 723001,China

In last decades,there has been much effort on the solution and the analysis of the nonlinear complementarity problem （NCP） by reformulating NCP as an unconstrained *** this paper,we propose a new method for the NCP under the condition that the solution *** formulate the NCP into a multiobjective optimization problem （MOP）,and define zero-efficient solution of *** we indicate that zero-efficient solution of the MOP is also the solution to the *** we use minimax method for the *** results indicate that the proposed method is promising.

关键词： nonlinear complementarity problem Multiobjective optimization problem Zero-efficient solution Minimax method

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Journal of Computational Mathematics 2003年第6期21卷 747-758页

作者： Chang-fengMa Pu-yanNie Guo-pingLiang DepartmentofComputationalScienceandAppliedPhysics GuilinInstituteofElectronicTechnologyGuangxi541004China DepartmentofMathematics InstituteofInformationScienceandTechnologyJinanUniversityGuangzhou510623China InstituteofMathematics AcademyofMathematicsandSystemSciencesChineseAcademyofSciencesBeijing100080China

The nonlinear complementarity problem can be reformulated as a nonsmooth equation. In this paper we propose a new smoothing Newton algorithm for the solution of the nonlinear complementarity problem by constructing a new smoothing approximation function. Global and local superlinear convergence results of the algorithm are obtained under suitable conditions. Numerical experiments confirm the good theoretical properties of the algorithm.

关键词： nonlinear complementarity problem Smoothing Newton method Global convergence Superlinear convergence.

A Class of New Large-Update Primal-Dual Interior-Point Algorithms for P＊（k） nonlinear complementarity problems

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Acta Mathematica Sinica,English Series 2011年第10期27卷 1979-1994页

作者： Hua Ping CHEN Ming Wang ZHANG College of Science China Three Gorges University Yichang 443002 P. R. China

In this paper we propose a class of new large-update primal-dual interior-point algorithms for P.（k） nonlinear complementarity problem （NCP）, which are based on a class of kernel functions investigated by Bai et al. in their recent work for linear optimization （LO）. The arguments for the algorithms are followed as Peng et al.＇s for P.（n） complementarity problem based on the self-regular functions [Peng, J., Roos, C., Terlaky, T.： Self-Regularity： A New Paradigm for Primal-Dual Interior- Point Algorithms, Princeton University Press, Princeton, 2002]. It is worth mentioning that since this class of kernel functions includes a class of non-self-regular functions as special case, so our algorithms are different from Peng et al.＇s and the corresponding analysis is simpler than theirs. The ultimate goal of the paper is to show that the algorithms based on these functions have favorable polynomial complexity.

关键词： Large-update method interior-point algorithm nonlinear complementarity problem non- self-regular function polynomial complexity

A Null Space Approach for Solving nonlinear complementarity problems

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Acta Mathematicae Applicatae Sinica 2006年第1期22卷 9-20页

作者： Pu-yan Nie Department of Mathematics College of Information Science and Technology Jinan University Guangzhou 510632 China

In this work, null space techniques are employed to tackle nonlinear complementarity problems （NCPs）. NCP conditions are transform into a nonlinear programming problem, which is handled by null space algorithms, The NCP conditions are divided into two groups, Some equalities and inequalities in an NCP are treated as constraints, While other equalities and inequalities in an NCP are to be regarded as objective function. Two groups are all updated in every step. Null space approaches are extended to nonlinear complementarity problems. Two different solvers are employed for all NCP in an algorithm.

关键词： Global convergence nonlinear complementarity problem nonlinear programming null space methods

A SQP METHOD FOR GENERAL nonlinear complementarity problemS

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Applied Mathematics(A Journal of Chinese Universities) 2000年第4期15卷 433-442页

作者： Xiu Naihua.Dept.of Appl.Math.,Northern Jiaotong Univ.,Beijing 100044. Email:nhxiu@*** Dept. of Appl. Math. Northern Jiaotong Univ. Beijing

In this paper,the nonlinear complementarity problem is transformed into the least squares problem with nonnegative constraints,and a SQP algorithm for this reformulation based on a damped Gauss Newton type method is *** is shown that the algorithm is globally and locally superlinearly (quadratically) convergent without the assumption of monotonicity.

关键词： nonlinear complementarity problem SQP method superlinear convergence quadratic convergence.