On the Rate of Local Convergence of High-Order-Infeasible-Path-Following Algorithms for P*-Linear Complementarity Problems

Authors:
Gongyun Zhao;Jie Sun
Affiliations:
Department of Mathematics, National University of Singapore, 119260, Singapore. matzgy@math.nus.edu.sg;Department of Decision Sciences, National University of Singapore, 119260, Singapore. jsun@nus.edu.sg
Venue:
Computational Optimization and Applications
Year:
1999

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Abstract

A simple and unified analysis is provided on the rate of local convergence for a class of high-order-infeasible-path-following algorithms for the P_*-linear complementarity problem (P_*-LCP). It is shown that therate of local convergence of a ν-order algorithm with a centering step is ν + 1 if there is a strictly complementary solution and(ν + 1)/2 otherwise. For the ν-order algorithm without thecentering step the corresponding rates are ν and ν/2, respectively. The algorithm without a centering step does not follow the fixed traditional central path.Instead, at each iteration, it follows a new analyticpath connecting the current iterate with an optimal solution to generate the next iterate. An advantage of this algorithm is that it does not restrict iterates in a sequence of contracting neighborhoods of the central path.