Convergence Analysis of an Infeasible Interior Point Algorithm Based on a Regularized Central Path for Linear Complementarity Problems

Authors:
Guanglu Zhou;Kim-Chuan Toh;Gongyun Zhao
Affiliations:
Department of Mathematics and Statistics, Curtin University of Technology, WA 6102, Australia. zhouguan@maths.curtin.edu.au;Department of Mathematics, National University of Singapore, 2 Science Drive 2, Singapore 117543. mattohkc@nus.edu.sg;Department of Mathematics, National University of Singapore, 2 Science Drive 2, Singapore 117543. matzgy@nus.edu.sg
Venue:
Computational Optimization and Applications
Year:
2004

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Abstract

Most existing interior-point methods for a linear complementarity problem (LCP) require the existence of a strictly feasible point to guarantee that the iterates are bounded. Based on a regularized central path, we present an infeasible interior-point algorithm for LCPs without requiring the strict feasibility condition. The iterates generated by the algorithm are bounded when the problem is a P* LCP and has a solution. Moreover, when the problem is a monotone LCP and has a solution, we prove that the convergence rate is globally linear and it achieves ε-feasibility and ε-complementarity in at most O(n2 ln(1/ε)) iterations with a properly chosen starting point.