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Further Application of -Differentiability to Generalized Complementarity Problems Based on Generalized Fisher-Burmeister Functions

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  • Wei-Zhe Gu
  • Mohamed A. Tawhid

Abstract

We study nonsmooth generalized complementarity problems based on the generalized Fisher-Burmeister function and its generalizations, denoted by GCP( ) where and are -differentiable. We describe -differentials of some GCP functions based on the generalized Fisher-Burmeister function and its generalizations, and their merit functions. Under appropriate conditions on the -differentials of and , we show that a local/global minimum of a merit function (or a “stationary point” of a merit function) is coincident with the solution of the given generalized complementarity problem. When specializing GCP to the nonlinear complementarity problems, our results not only give new results but also extend/unify various similar results proved for , semismooth, and locally Lipschitzian.

Suggested Citation

  • Wei-Zhe Gu & Mohamed A. Tawhid, 2014. "Further Application of -Differentiability to Generalized Complementarity Problems Based on Generalized Fisher-Burmeister Functions," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-11, November.
    • Handle: RePEc:hin:jnlaaa:468065
    DOI: 10.1155/2014/468065
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