A matrix-splitting method for symmetric affine second-order cone complementarity problems

Authors:
Shunsuke Hayashi;Takahiro Yamaguchi;Nobuo Yamashita;Masao Fukushima
Affiliations:
Department of Applied Mathematics and Physics, Graduate School of Informatics, Kyoto University, Kyoto 606-8501, Japan;Department of Applied Mathematics and Physics, Graduate School of Informatics, Kyoto University, Kyoto 606-8501, Japan;Department of Applied Mathematics and Physics, Graduate School of Informatics, Kyoto University, Kyoto 606-8501, Japan;Department of Applied Mathematics and Physics, Graduate School of Informatics, Kyoto University, Kyoto 606-8501, Japan
Venue:
Journal of Computational and Applied Mathematics
Year:
2005

Citing 16
Cited 1

Matrix analysis

Matrix analysis
Parallel successive overrelaxation methods for symmetric linear complementarity problems and linear programs

Journal of Optimization Theory and Applications
Asynchronous parallel successive overrelaxation for the symmetric linear complementarity problem

Mathematical Programming: Series A and B
Finite-dimensional variational inequality and nonlinear complementarity problems: a survey of theory, algorithms and applications

Mathematical Programming: Series A and B
Scientific computing: an introduction with parallel computing

Scientific computing: an introduction with parallel computing
On the convergence of iterative methods for symmetric linear complementarity problems

Mathematical Programming: Series A and B
A multisplitting method for symmetric linear complementarity problems

Journal of Computational and Applied Mathematics
Smoothing methods for convex inequalities and linear complementarity problems

Mathematical Programming: Series A and B
Matrix computations (3rd ed.)

Matrix computations (3rd ed.)
Trust-region methods

Trust-region methods
Weighted max-norm estimate of additive Schwarz iteration scheme for solving linear complementarity problems

Journal of Computational and Applied Mathematics
Smoothing Functions for Second-Order-Cone Complementarity Problems

SIAM Journal on Optimization
Jacobian Smoothing Methods for Nonlinear Complementarity Problems

SIAM Journal on Optimization
Smoothing functions and smoothing Newton method for complementarity and variational inequality problems

Journal of Optimization Theory and Applications
Complementarity Functions and Numerical Experiments on Some Smoothing Newton Methods for Second-Order-Cone Complementarity Problems

Computational Optimization and Applications
A Combined Smoothing and Regularization Method for Monotone Second-Order Cone Complementarity Problems

SIAM Journal on Optimization

A multisplitting method for symmetrical affine second-order cone complementarity problem

Computers & Mathematics with Applications

Quantified Score

Hi-index	7.29

Visualization

Abstract

The affine second-order cone complementarity problem (SOCCP) is a wide class of problems that contains the linear complementarity problem (LCP) as a special case. The purpose of this paper is to propose an iterative method for the symmetric affine SOCCP that is based on the idea of matrix splitting. Matrix-splitting methods have originally been developed for the solution of the system of linear equations and have subsequently been extended to the LCP and the affine variational inequality problem. In this paper, we first give conditions under which the matrix-splitting method converges to a solution of the affine SOCCP. We then present, as a particular realization of the matrix-splitting method, the block successive overrelaxation (SOR) method for the affine SOCCP involving a positive definite matrix, and propose an efficient method for solving subproblems. Finally, we report some numerical results with the proposed algorithm, where promising results are obtained especially for problems with sparse matrices.