Abstract

Most asymptotic convergence analysis of interior-point algorithms for monotone linear complementarity problems assumes that the problem is nondegenerate, that is, the solution set contains a strictly complementary solution. We investigate the behavior of these algorithms when this assumption is removed. 1 Introduction In the monotone linear complementarity problem (LCP), we seek a vector pair (x; y) 2 IR n \Theta IR n that satisfies the conditions y = Mx+ q; x 0; y 0; x T y = 0; (1) where q 2 IR n , and M 2 IR n\Thetan is positive semidefinite. We use S to denote the solution set of (1). An assumption that is frequently made in order to prove superlinear convergence of interior-point algorithms for (1) is the nondegeneracy assumption: Assumption 1 There is an (x ; y ) 2 S such that x i + y i ? 0 for all i = 1; \Delta \Delta \Delta ; n. In general, we can define three subsets B, N , and J of the index set f1; \Delta \Delta \Delta ; ng by B = fi = 1; \Delta ...

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