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Properties of Restricted NCP Functions for Nonlinear Complementarity Problems

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  • N. Yamashita

    (Kyoto University)

Abstract

In this paper, we study restricted NCP functions which may be used to reformulate the nonlinear complementarity problem as a constrained minimization problem. In particular, we consider three classes of restricted NCP functions, two of them introduced by Solodov and the other proposed in this paper. We give conditions under which a minimization problem based on a restricted NCP function enjoys favorable properties, such as equivalence between a stationary point of the minimization problem and the nonlinear complementarity problem, strict complementarity at a solution of the minimization problem, and boundedness of the level sets of the objective function. We examine these properties for three restricted NCP functions and show that the merit function based on the restricted NCP function proposed in this paper enjoys favorable properties compared with those based on the other restricted NCP functions.

Suggested Citation

  • N. Yamashita, 1998. "Properties of Restricted NCP Functions for Nonlinear Complementarity Problems," Journal of Optimization Theory and Applications, Springer, vol. 98(3), pages 701-717, September.
    • Handle: RePEc:spr:joptap:v:98:y:1998:i:3:d:10.1023_a:1022684215427
    DOI: 10.1023/A:1022684215427
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    References listed on IDEAS

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    1. C. Kanzow & N. Yamashita & M. Fukushima, 1997. "New NCP-Functions and Their Properties," Journal of Optimization Theory and Applications, Springer, vol. 94(1), pages 115-135, July.
    2. F. Facchinei & C. Kanzow, 1997. "On Unconstrained and Constrained Stationary Points of the Implicit Lagrangian," Journal of Optimization Theory and Applications, Springer, vol. 92(1), pages 99-115, January.
    3. M. V. Solodov, 1997. "Stationary Points of Bound Constrained Minimization Reformulations of Complementarity Problems," Journal of Optimization Theory and Applications, Springer, vol. 94(2), pages 449-467, August.
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    Cited by:

    1. Azam Asanjarani, 2023. "A Finsler Geometrical Programming Approach to the Nonlinear Complementarity Problem of Traffic Equilibrium," Journal of Optimization Theory and Applications, Springer, vol. 196(3), pages 797-809, March.
    2. Liyan Xu & Bo Yu, 2014. "CVaR-constrained stochastic programming reformulation for stochastic nonlinear complementarity problems," Computational Optimization and Applications, Springer, vol. 58(2), pages 483-501, June.
    3. S. Mohsen Miri & Sohrab Effati, 2015. "On Generalized Convexity of Nonlinear Complementarity Functions," Journal of Optimization Theory and Applications, Springer, vol. 164(2), pages 723-730, February.
    4. Aurél Galántai, 2012. "Properties and construction of NCP functions," Computational Optimization and Applications, Springer, vol. 52(3), pages 805-824, July.

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