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An $$ \mathcal{O} $$ (rL) infeasible interior-point algorithm for symmetric cone LCP via CHKS function

An $$ \mathcal{O} $$ (rL) infeasible interior-point algorithm for symmetric cone LCP via CHKS... In this paper, we propose a theoretical framework of an infeasible interior-point algorithm for solving monotone linear complementarity problems over symmetric cones (SCLCP). The new algorithm gets Newton-like directions from the Chen-Harker-Kanzow-Smale (CHKS) smoothing equation of the SCLCP. It possesses the following features: The starting point is easily chosen; one approximate Newton step is computed and accepted at each iteration; the iterative point with unit stepsize automatically remains in the neighborhood of central path; the iterative sequence is bounded and possesses $$ \mathcal{O} $$ (rL) polynomial-time complexity under the monotonicity and solvability of the SCLCP. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Mathematicae Applicatae Sinica Springer Journals

An $$ \mathcal{O} $$ (rL) infeasible interior-point algorithm for symmetric cone LCP via CHKS function

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Publisher
Springer Journals
Copyright
Copyright © 2009 by Institute of Applied Mathematics, Academy of Mathematics and System Sciences, Chinese Academy of Sciences and Springer Berlin Heidelberg
Subject
Mathematics; Theoretical, Mathematical and Computational Physics; Math Applications in Computer Science; Applications of Mathematics
ISSN
0168-9673
eISSN
1618-3932
DOI
10.1007/s10255-008-8814-2
Publisher site
See Article on Publisher Site

Abstract

In this paper, we propose a theoretical framework of an infeasible interior-point algorithm for solving monotone linear complementarity problems over symmetric cones (SCLCP). The new algorithm gets Newton-like directions from the Chen-Harker-Kanzow-Smale (CHKS) smoothing equation of the SCLCP. It possesses the following features: The starting point is easily chosen; one approximate Newton step is computed and accepted at each iteration; the iterative point with unit stepsize automatically remains in the neighborhood of central path; the iterative sequence is bounded and possesses $$ \mathcal{O} $$ (rL) polynomial-time complexity under the monotonicity and solvability of the SCLCP.

Journal

Acta Mathematicae Applicatae Sinica – Springer Journals

Published: Sep 8, 2009

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