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Florian A. Potra (potramath.umbc.edu) Abstract: Two correctorpredictor 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, interiorpoint 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: 03/31/2006 Modify/Update this entry  
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