- Interior point methods for sufficient LCP in a wide neighborhood of the central path with optimal iteration complexity Florian A. Potra(potraumbc.edu) Abstract: Three interior point methods are proposed for sufficient horizontal linear complementarity problems (HLCP): a large update path following algorithm, a first order corrector-predictor method, and a second order corrector-predictor method. All algorithms produce sequences of iterates in the wide neighborhood of the central path introduced by Ai and Zhang. The algorithms do not depend on the handicap $\kappa$ of the problem, so that they can be used for any sufficient HLCP. They have $O((1+\kappa)\sqrt{n}L)$ iteration complexity, the best iteration complexity obtained so far by any interior point method for solving sufficient linear complementarity problems. The first order corrector-predictor method is Q-quadratically convergent for problem that have a strict complementarity solution. The second order corrector-predictor method is superlinearly convergent with Q order 1.5 for general problems, and with Q order 3 for problems that have a strict complementarity solution. Keywords: linear complementarity, interior point, path-following, corrector-predictor, sufficient matrix, wide neighborhood Category 1: Complementarity and Variational Inequalities Category 2: Linear, Cone and Semidefinite Programming Citation: Technical Report, Department of Mathematics and Statistics, University of Maryland Baltimore County, 1000 Hilltop Circle, Baltimore, MD 21250, July, 2012 Download: [PDF]Entry Submitted: 07/11/2012Entry Accepted: 07/11/2012Entry Last Modified: 07/11/2012Modify/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 Optmization Society.