非線形相補性問題に対する近接点法

概要

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The paper of this article is to describe a proximal point algorithm (PPA) for solving the nonlinear complementarity problem (NCP). PPA was originally proposed by Martinet and further developed by Rockafellar for monotone operator problems. It is known to have nice convergence properties under appropriate criteria for approximate solutions of subproblems. However, it is not always easy to solve subproblems or to check those criteria. Moreover, PPA has been applied mainly to monotone problems. In this article, we present a PPA for the NCP involving a Po function and establish its global convergence under appropriate conditions by using the results derived from the reformulation approach for NCP. Moreover, without assuming the local uniqueness of the solution, we show that the rate of convergence is superlinear in a genuine sense.
日本応用数理学会の論文
2000-03-15