线性互补问题的一个推广

Journal of Combinatorial Theory Pub Date : 1970-01-01 DOI:10.1016/S0021-9800(70)80010-2

Richard W. Cottle , George B. Dantzig

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引用次数: 171

摘要

线性互补问题:发现z∈Rp满足w=q+Mzw大于或等于0,z大于或等于0(LCP)zTw=0被推广到矩阵M不是平方的问题。给出了一种类似于c.e. Lemke(1965)的求解方法(LCP)的解法。本文从图论的观点讨论了该方法，并与d.i.a. Cohen(1967)对Sperner引理的证明和H. Scarf(1967)关于逼近单纯形到自身的连续映射的不动点的一些工作密切相关。

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A generalization of the linear complementarity problem

The linear complementarity problem: find z∈R^p satisfying $\begin{matrix} w = q + M z \\ w ⩾ 0, z ⩾ 0 (LCP) \\ z^{T} w = 0 \end{matrix}$ is generalized to a problem in which the matrix M is not square. A solution technique similar to C. E. Lemke's (1965) method for solving (LCP) is given. The method is discussed from a graph-theoretic viewpoint and closely parallels a proof of Sperner's lemma by D. I. A. Cohen (1967) and some work of H. Scarf (1967) on approximating fixed points of a continuous mapping of a simplex into itself.

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Journal of Combinatorial Theory

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