Convergence Analysis of an Infeasible Interior Point Algorithm Based on a Regularized Central Path for Linear Complementarity Problems Guanglu Zhou Kim-Chuan Toh + and Gongyun Zhao
BibTeX
@MISC{April_convergenceanalysis,
author = {August Revised April and Guanglu Zhou and Kim-chuan Toh and Gongyun Zhao},
title = {Convergence Analysis of an Infeasible Interior Point Algorithm Based on a Regularized Central Path for Linear Complementarity Problems Guanglu Zhou Kim-Chuan Toh + and Gongyun Zhao},
year = {}
}
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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 #-feasibility and #- complementarity in at most O(n ln(1/#)) iterations with a properly chosen starting point.
