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On stationary points of the implicit Lagrangian for nonlinear complementarity problems

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Abstract

Mangasarian and Solodov have recently introduced an unconstrained optimization problem whose global minima are solutions of the nonlinear complementarity problem (NCP). In this paper, we show that, if the mapping involved in NCP has a positive-definite Jacobian, then any stationary point of the optimization problem actually solves NCP. We also discuss a descent method for solving the unconstrained optimization problem.

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Authors and Affiliations

  1. Graduate School of Information Science, Nara Institute of Science and Technology, Ikoma, Nara, Japan

    N. Yamashita (Graduate Student) & M. Fukushima (Professor)

Authors
  1. N. Yamashita
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  2. M. Fukushima
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Additional information

Communicated by O. L. Mangasarian

The authors are indebted to a referee for a helpful suggestion that led them to develop the descent method described in Section 3. They are grateful to Professor F. Facchinei, who kindly pointed out an error in the proof of Theorem 2.3 in an earlier version of the paper. The also thank Professor P. Tseng for a discussion on Theorem 3.1.

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Yamashita, N., Fukushima, M. On stationary points of the implicit Lagrangian for nonlinear complementarity problems. J Optim Theory Appl 84, 653–663 (1995). https://doi.org/10.1007/BF02191990

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