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Title: A Smoothing-Type Algorithm for Solving Linear Complementarity Problems with Strong Convergence Properties

Abstract

In this paper, we construct an augmented system of the standard monotone linear complementarity problem (LCP), and establish the relations between the augmented system and the LCP. We present a smoothing-type algorithm for solving the augmented system. The algorithm is shown to be globally convergent without assuming any prior knowledge of feasibility/infeasibility of the problem. In particular, if the LCP has a solution, then the algorithm either generates a maximal complementary solution of the LCP or detects correctly solvability of the LCP, and in the latter case, an existing smoothing-type algorithm can be directly applied to solve the LCP without any additional assumption and it generates a maximal complementary solution of the LCP; and that if the LCP is infeasible, then the algorithm detect correctly infeasibility of the LCP. To the best of our knowledge, such properties have not appeared in the existing literature for smoothing-type algorithms.

Authors:
 [1]
  1. Tianjin University, Department of Mathematics, School of Science (China)
Publication Date:
OSTI Identifier:
21067394
Resource Type:
Journal Article
Journal Name:
Applied Mathematics and Optimization
Additional Journal Information:
Journal Volume: 57; Journal Issue: 1; Other Information: DOI: 10.1007/s00245-007-9004-y; Copyright (c) 2008 Springer Science+Business Media, LLC; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0095-4616
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ALGORITHMS; CONVERGENCE; MATHEMATICAL SOLUTIONS

Citation Formats

Huang Zhenghai, E-mail: huangzhenghai@tju.edu.cn, and Weizhe, Gu. A Smoothing-Type Algorithm for Solving Linear Complementarity Problems with Strong Convergence Properties. United States: N. p., 2008. Web. doi:10.1007/S00245-007-9004-Y.
Huang Zhenghai, E-mail: huangzhenghai@tju.edu.cn, & Weizhe, Gu. A Smoothing-Type Algorithm for Solving Linear Complementarity Problems with Strong Convergence Properties. United States. https://doi.org/10.1007/S00245-007-9004-Y
Huang Zhenghai, E-mail: huangzhenghai@tju.edu.cn, and Weizhe, Gu. Fri . "A Smoothing-Type Algorithm for Solving Linear Complementarity Problems with Strong Convergence Properties". United States. https://doi.org/10.1007/S00245-007-9004-Y.
@article{osti_21067394,
title = {A Smoothing-Type Algorithm for Solving Linear Complementarity Problems with Strong Convergence Properties},
author = {Huang Zhenghai, E-mail: huangzhenghai@tju.edu.cn and Weizhe, Gu},
abstractNote = {In this paper, we construct an augmented system of the standard monotone linear complementarity problem (LCP), and establish the relations between the augmented system and the LCP. We present a smoothing-type algorithm for solving the augmented system. The algorithm is shown to be globally convergent without assuming any prior knowledge of feasibility/infeasibility of the problem. In particular, if the LCP has a solution, then the algorithm either generates a maximal complementary solution of the LCP or detects correctly solvability of the LCP, and in the latter case, an existing smoothing-type algorithm can be directly applied to solve the LCP without any additional assumption and it generates a maximal complementary solution of the LCP; and that if the LCP is infeasible, then the algorithm detect correctly infeasibility of the LCP. To the best of our knowledge, such properties have not appeared in the existing literature for smoothing-type algorithms.},
doi = {10.1007/S00245-007-9004-Y},
url = {https://www.osti.gov/biblio/21067394}, journal = {Applied Mathematics and Optimization},
issn = {0095-4616},
number = 1,
volume = 57,
place = {United States},
year = {2008},
month = {2}
}