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Properties and construction of NCP functions

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  • Aurél Galántai

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    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

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    File URL: http://hdl.handle.net/10.1007/s10589-011-9428-9
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    Bibliographic Info

    Article provided by Springer in its journal Computational Optimization and Applications.

    Volume (Year): 52 (2012)
    Issue (Month): 3 (July)
    Pages: 805-824

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    Handle: RePEc:spr:coopap:v:52:y:2012:i:3:p:805-824

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    Web page: http://www.springer.com/math/journal/10589

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    Related research

    Keywords: Nonlinear complementarity problem; NCP function; Nonlinear equation; Merit function;

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    1. Jein-Shan Chen, 2007. "On Some Ncp-Functions Based On The Generalized Fischer–Burmeister Function," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 24(03), pages 401-420.
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