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SIAMJO
2008

Primal-Dual Affine Scaling Interior Point Methods for Linear Complementarity Problems

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Primal-Dual Affine Scaling Interior Point Methods for Linear Complementarity Problems
A first order affine scaling method and two mth order affine scaling methods for solving monotone linear complementarity problems (LCP) are presented. All three methods produce iterates in a wide neighborhood of the central path. The first order method has O(nL2(log nL2)(log log nL2)) iteration complexity. If the LCP admits a strict complementary solution then both the duality gap and the iteration sequence converge superlinearly with Q-order two. If m = (log( nL)), then both higher order methods have O( n)L iteration complexity. The Q-order of convergence of one of the methods is (m + 1) for problems that admit a strict complementarity solution while the Q-order of convergence of the other method is (m + 1)/2 for general monotone LCPs. Key words. linear complementarity, interior-point, affine scaling, large neighborhood, superlinear convergence AMS subject classifications. 90C51, 65K05, 49M15, 90C05, 90C20
Florian A. Potra
Added 14 Dec 2010
Updated 14 Dec 2010
Type Journal
Year 2008
Where SIAMJO
Authors Florian A. Potra
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