Frontiers of Mathematics in China >

2006 , Vol. 1 >Issue 3: 368 - 381

DOI: https://doi.org/10.1007/s11464-006-0015-9

New multiplier method for solving linear complementarity problems

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  • 1.Department of Mathematics, College of Science and Technology, Inner Mongolia University, Hohhot 010021, China; Department of Mathematics, College of Science, Inner Mongolia University ofTechnology, Hohhot 010051, China; 2.Department of Mathematics, College of Science, Inner Mongolia University of Technology, Hohhot 010051, China;

Published date: 05 Sep 2006

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Abstract

A new multiplier method for solving the linear complementarity problem LCP(q,M) is proposed. By introducing a Lagrangian of LCP(q,M), a new smooth merit function θ(χ, λ) for LCP(q,M) is constructed. Based on it, a simple damped Newton-type algorithm with multiplier self-adjusting step is presented. When M is a P-matrix, the sequence {θ(χk, λk)} (where {(χk, λk)} is generated by the algorithm) is globally linearly convergent to zero and convergent in a finite number of iterations if the solution is degenerate. Numerical results suggest that the method is highly effcient and promising.

Cite this article

Ulji, CHEN Guoqing . New multiplier method for solving linear complementarity problems[J]. Frontiers of Mathematics in China, 2006 , 1(3) : 368 -381 . DOI: 10.1007/s11464-006-0015-9

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