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An Algorithm for the Fast Solution of Linear Complementarity Problems

Jose Luis Morales(morales***at***eecs.northwestern.edu)
Jorge Nocedal(nocedal***at***eecs.northwestern.edu)
Mikhail Smelyanskiy(mikhail.smelyanskiy***at***intel.com)

Abstract: This paper studies algorithms for the solution of mixed symmetric linear complementarity problems. The goal is to compute fast and approximate solutions of medium to large sized problems, such as those arising in computer game simulations and American option pricing. The paper proposes an improvement of a method described by Kocvara and Zowe that combines projected Gauss-Seidel iterations with subspace minimization steps. The proposed algorithm employs a recursive subspace minimization designed to handle severely ill-conditioned problems. Numerical tests indicate that the approach is more efficient than interior-point and gradient projection methods on some physical simulation problems that arise in computer game scenarios.

Keywords: linear complementarity, optimization, rigid body simulation

Category 1: Complementarity and Variational Inequalities

Citation: Report 2007/5 Optimization Technology Center, Northwestern University, June 2007

Download: [PDF]

Entry Submitted: 06/05/2007
Entry Accepted: 06/06/2007
Entry Last Modified: 06/05/2007

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