Corrector-predictor methods for sufficient linear complementarity problems

Filiz Gürtuna, Cosmin G. Petra, Florian A. Potra, Olena Shevchenko, Adrian Vancea

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 κ 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+κ)2 nL)-iteration complexity for “sufficiently large” infeasible starting points.