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2006•SIAM Journal on OptimizationRequires access

Corrector‐Predictor Methods for Sufficient Linear Complementarity Problems in a Wide Neighborhood of the Central Path

Xing Liu, Florian Alexandru Potra

Open publisher page 32 citations

Abstract

A higher order corrector‐predictor interior‐point method is proposed for solving sufficient linear complementarity problems. The algorithm produces a sequence of iterates in the $\caln_{\infty}^{-}$ neighborhood of the central path. The algorithm does not depend on the handicap κ of the problem. It has $O((1+\kappa)\sqrt{n}L)$ iteration complexity and is superlinearly convergent even for degenerate problems.

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What this paper is about

A higher order corrector‐predictor interior‐point method is proposed for solving sufficient linear complementarity problems. The algorithm produces a sequence of iterates in the $\caln_{\infty}^{-}$ neighborhood of the central path. The algorithm does not depend on the handicap κ of the problem. It has $O((1+\kappa)\sqrt{n}L)$ iteration complexity and is superlinearly convergent even for degenerate problems.

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Available abstract

A higher order corrector‐predictor interior‐point method is proposed for solving sufficient linear complementarity problems. The algorithm produces a sequence of iterates in the $\caln_{\infty}^{-}$ neighborhood of the central path. The algorithm does not depend on the handicap κ of the problem. It has $O((1+\kappa)\sqrt{n}L)$ iteration complexity and is superlinearly convergent even for degenerate problems.

Key concepts: Mathematics, Iterated function, Complementarity (molecular biology), Interior point method, Predictor–corrector method, Linear complementarity problem, Degenerate energy levels, Path (computing)

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