Interior Point Methods for Sufficient Lcp in a Wide Neighborhood of the Central Path with Optimal Iteration Complexity
نویسنده
چکیده
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 κ of the problem, so that they can be used for any sufficient HLCP. They have O((1 + κ) √ nL) 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.
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