Corrector-predictor methods for sufficient linear complementarity problems

Authors:
Filiz Gurtuna;Cosmin Petra;Florian A. Potra;Olena Shevchenko;Adrian Vancea
Affiliations:
Department of Mathematics & Statistics, University of Maryland, Baltimore, USA 21250;Department of Mathematics & Statistics, University of Maryland, Baltimore, USA 21250;Department of Mathematics & Statistics, University of Maryland, Baltimore, USA 21250;Department of Mathematics, Western Michigan University, Kalamazoo, USA 49008-5248;Department of Mathematics & Statistics, University of Maryland, Baltimore, USA 21250
Venue:
Computational Optimization and Applications
Year:
2011

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Abstract

We present a new corrector-predictor method for solving sufficient linear complementarity problems for which a sufficiently centered feasible starting point is available. In contrast with its predictor-corrector counterpart proposed by Miao, the method does not depend on the handicap 驴 of the problem. The method has $O((1+\kappa)\sqrt{n}L)$ -iteration complexity, the same as Miao's method, but our error estimates are sightly better. The algorithm is quadratically convergent for problems having a strictly complementary solution. We also present a family of infeasible higher order corrector-predictor methods that are superlinearly convergent even in the absence of strict complementarity. The algorithms of this class are globally convergent for general positive starting points. They have $O((1+\kappa)\sqrt{n}L)$ -iteration complexity for feasible, or "almost feasible", starting points and O((1+驴)2 nL)-iteration complexity for "sufficiently large" infeasible starting points.