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Further Application of H‐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(f, g) where f and g are H‐differentiable. We describe H‐differentials of some GCP functions based on the generalized Fisher‐Burmeister function and its generalizations, and their merit functions. Under appropriate conditions on the H‐differentials of f and g, 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(f, g) to the nonlinear complementarity problems, our results not only give new results but also extend/unify various similar results proved for C1, semismooth, and locally Lipschitzian.

Suggested Citation

  • Wei-Zhe Gu & Mohamed A. Tawhid, 2014. "Further Application of H‐Differentiability to Generalized Complementarity Problems Based on Generalized Fisher‐Burmeister Functions," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    • Handle: RePEc:wly:jnlaaa:v:2014:y:2014:i:1:n:468065
    DOI: 10.1155/2014/468065
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    References listed on IDEAS

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    2. Liqun Qi, 1993. "Convergence Analysis of Some Algorithms for Solving Nonsmooth Equations," Mathematics of Operations Research, INFORMS, vol. 18(1), pages 227-244, February.
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