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- W1990665670 abstract "Zhang and Tapia have recently developed an interior-point algorithm for the linear programming problem that has the property that the duality gap converges to zero q-quadratically in the nondegenerate case and (if the iterates converge) q-superlinearly in the degenerate case. Their algorithm also solves the integer model for LP in $O ( nL )$ iterations, where L is the input length of the LP This paper presents an algorithm which maintains the quadratic (superlinear) convergence property but solves LP in $O ( sqrt{n} L )$ iterations in the integer model. Also, the algorithm is generalized into an algorithm which solves LCP. The LCP algorithm (which is similar to an adaptive path-following algorithm proposed by Mizuno, Yoshise, and Kikuchi) has similar local convergence properties if we assume that the iterates converge to a strictly complementary solution." @default.
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- W1990665670 date "1994-05-01" @default.
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- W1990665670 title "Superlinearly Convergent $O ( sqrt{n} L )$-Iteration Interior-Point Algorithms for Linear Programming and the Monotone Linear Complementarity Problem" @default.
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- W1990665670 doi "https://doi.org/10.1137/0804014" @default.
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