- Corrector-predictor methods for monotone linear complementarity problems in a wide neighborhood of the central path Florian A. Potra (potramath.umbc.edu) Abstract: Two corrector-predictor interior point algorithms are proposed for solving mono\-tone linear complementarity problems. The algorithms produce a sequence of iterates in the $\caln_{\infty}^{-}$ neighborhood of the central path. The first algorithm uses line search schemes requiring the solution of higher order polynomial equations in one variable, while the line search procedures of the second algorithm can be implemented in $O(m\, n^{1+\alpha})$ arithmetic operations, where $n$ is the dimension of the problems, $\alpha\in(0,1]$ is a constant, and $m$ is the maximum order of the predictor and the corrector. If $m=\Omega(\log n)$ then both algorithms have $O(\sqrt{n}L)$ iteration complexity. They are superlinearly convergent even for degenerate problems. Keywords: linear complementarity problem, interior-point algorithm, large neighbourhood, superlinear convergence Category 1: Complementarity and Variational Inequalities Category 2: Linear, Cone and Semidefinite Programming Citation: Technical Report, UMBC, September 2004, Revised: February, 2006. Download: [PDF]Entry Submitted: 03/31/2006Entry Accepted: 04/02/2006Entry Last Modified: 03/31/2006Modify/Update this entry Visitors Authors More about us Links Subscribe, Unsubscribe Digest Archive Search, Browse the Repository Submit Update Policies Coordinator's Board Classification Scheme Credits Give us feedback Optimization Journals, Sites, Societies Optimization Online is supported by the Mathematical Programming Society and by the Optimization Technology Center.