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Keywords
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Interior-point methods, linear complementarity problem, P(k) matrix, wide neighborhood, polynomial complexity
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Abstract
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In this paper, we propose a second-order corrector interior-point algorithm for solving P(k)
linear complementarity problems. The method generates a sequence of iterates in a wide neighborhood of
the central path introduced by Ai and Zhang. In each iteration, the method computes a corrector direction in
addition to the Ai-Zhang direction, in an attempt to improve performance. The algorithm does not depend
on the handicap of the problem, so that it can be used for any P(k)–linear complementarity problems. It
is shown that the iteration complexity bound of the algorithm is O(1 + k)3 pnL. Some numerical results
are provided to illustrate the performance of the algorithm.
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