The Proximal Point Algorithm for the P0 Complementarity Problem

  • Nobuo Yamashita
  • Junji Imai
  • Masao Fukushima
Part of the Applied Optimization book series (APOP, volume 50)


In this paper we consider a proximal point algorithm (PPA) for solving the nonlinear complementarity problem (NCP) with a P 0 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 P 0 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.


nonlinear complementarity problem proximal point algorithm P0 function 


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Copyright information

© Springer Science+Business Media Dordrecht 2001

Authors and Affiliations

  • Nobuo Yamashita
    • 1
  • Junji Imai
    • 1
  • Masao Fukushima
    • 2
  1. 1.Toyota Central R&D Labs., Inc.Nagakute, Nagakute-cho, Aichi-gun, AichiJapan
  2. 2.Department of Applied Mathematics and Physics, Graduate School of InformaticsKyoto UniversityKyotoJapan

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