2001 | OriginalPaper | Buchkapitel
The Proximal Point Algorithm for the P 0 Complementarity Problem
verfasst von : Nobuo Yamashita, Junji Imai, Masao Fukushima
Erschienen in: Complementarity: Applications, Algorithms and Extensions
Verlag: Springer US
Enthalten in: Professional Book Archive
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In this paper we consider a proximal point algorithm (PPA) for solving the nonlinear complementarity problem (NCP) with a P0 function. PPA was originally proposed by Martinet and further developed by Rockafellar for monotone variational inequalities and monotone operator problems. PPA is known to have nice convergence properties under mild conditions. However, until now, it has been applied mainly to monotone problems. In this paper, we propose a PPA for the NCP involving a P0 function and establish its global convergence under appropriate conditions by using the Mountain Pass Theorem. Moreover, we give conditions under which it has a superlinear rate of convergence.