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Properties and construction of NCP functions

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  • Aurél Galántai

Abstract

The nonlinear complementarity or NCP functions were introduced by Mangasarian and these functions are proved to be useful in constrained optimization and elsewhere. Interestingly enough there are only two general methods to derive such functions, while the known or used NCP functions are either individual constructions or modifications of the few individual NCP functions such as the Fischer-Burmeister function. In the paper we analyze the elementary properties of NCP functions and the various techniques used to obtain such functions from old ones. We also prove some new nonexistence results on the possible forms of NCP functions. Then we develop and analyze several new methods for the construction of nonlinear complementarity functions that are based on various geometric arguments or monotone transformations. The appendix of the paper contains the list and source of the known NCP functions. Copyright Springer Science+Business Media, LLC 2012

Suggested Citation

  • Aurél Galántai, 2012. "Properties and construction of NCP functions," Computational Optimization and Applications, Springer, vol. 52(3), pages 805-824, July.
    • Handle: RePEc:spr:coopap:v:52:y:2012:i:3:p:805-824
    DOI: 10.1007/s10589-011-9428-9
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. X. Chen & L. Qi & Y. F. Yang, 2002. "Lagrangian Globalization Methods for Nonlinear Complementarity Problems," Journal of Optimization Theory and Applications, Springer, vol. 112(1), pages 77-95, January.
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    Cited by:

    1. Johanna Burtscheidt & Matthias Claus, 2017. "A Note on Stability for Risk-Averse Stochastic Complementarity Problems," Journal of Optimization Theory and Applications, Springer, vol. 172(1), pages 298-308, January.

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