On NCP-Functions

Authors:
Defeng Sun;Liqun Qi
Affiliations:
School of Mathematics, the University of New South Wales, Sydney 2052, Australia. sun@maths.unsw.edu.au;School of Mathematics, the University of New South Wales, Sydney 2052, Australia. l.qi@unsw.edu.au
Venue:
Computational Optimization and Applications - Special issue on computational optimization—a tribute to Olvi Mangasarian, part II
Year:
1999

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Foreword

Computational Optimization and Applications

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Abstract

In this paper we reformulate several NCP-functionsfor the nonlinear complementarityproblem (NCP) from their merit function forms and studysome important properties of these NCP-functions. We point out thatsome of these NCP-functions have all the nice properties investigated by Chen, Chen and Kanzow [2] fora modified Fischer-Burmeister function, while some other NCP-functionsmay lose one or several of these properties. We alsoprovide a modified normal map and a smoothing technique toovercome the limitation of these NCP-functions. A numerical comparisonfor the behaviour of various NCP-functions is provided.