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A new class of complementarity functions for symmetric cone complementarity problems

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Abstract

A popular approach to solving the complementarity problem is to reformulate it as an equivalent equation system via a complementarity function. In this paper, we propose a new class of functions, which contains the penalized natural residual function and the penalized Fischer–Burmeister function for symmetric cone complementarity problems. We show that this class of functions is indeed a class of complementarity functions. We finally prove that the merit function of this new class of complementarity functions is coercive.

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Authors and Affiliations

  1. Department of Mathematics, Harbin Institute of Technology, Harbin, 150001, People’s Republic of China

    Yuan Min Li & Xing Tao Wang

  2. National Key Laboratory of Tunable Laser Technology, Harbin Institute of Technology, Harbin, 150001, People’s Republic of China

    De Yun Wei

Authors
  1. Yuan Min Li
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  2. Xing Tao Wang
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  3. De Yun Wei
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Correspondence to Yuan Min Li.

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Li, Y.M., Wang, X.T. & Wei, D.Y. A new class of complementarity functions for symmetric cone complementarity problems. Optim Lett 5, 247–257 (2011). https://doi.org/10.1007/s11590-010-0204-z

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  • DOI: https://doi.org/10.1007/s11590-010-0204-z

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