A SmoothingType 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 smoothingtype 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 smoothingtype 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 smoothingtype algorithms.
 Authors:

 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/s002450079004y; Copyright (c) 2008 Springer Science+Business Media, LLC; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 00954616
 Country of Publication:
 United States
 Language:
 English
 Subject:
 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ALGORITHMS; CONVERGENCE; MATHEMATICAL SOLUTIONS
Citation Formats
Huang Zhenghai, Email: huangzhenghai@tju.edu.cn, and Weizhe, Gu. A SmoothingType Algorithm for Solving Linear Complementarity Problems with Strong Convergence Properties. United States: N. p., 2008.
Web. doi:10.1007/S002450079004Y.
Huang Zhenghai, Email: huangzhenghai@tju.edu.cn, & Weizhe, Gu. A SmoothingType Algorithm for Solving Linear Complementarity Problems with Strong Convergence Properties. United States. https://doi.org/10.1007/S002450079004Y
Huang Zhenghai, Email: huangzhenghai@tju.edu.cn, and Weizhe, Gu. Fri .
"A SmoothingType Algorithm for Solving Linear Complementarity Problems with Strong Convergence Properties". United States. https://doi.org/10.1007/S002450079004Y.
@article{osti_21067394,
title = {A SmoothingType Algorithm for Solving Linear Complementarity Problems with Strong Convergence Properties},
author = {Huang Zhenghai, Email: 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 smoothingtype 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 smoothingtype 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 smoothingtype algorithms.},
doi = {10.1007/S002450079004Y},
url = {https://www.osti.gov/biblio/21067394},
journal = {Applied Mathematics and Optimization},
issn = {00954616},
number = 1,
volume = 57,
place = {United States},
year = {2008},
month = {2}
}