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Optimality Conditions for Nonsmooth Equilibrium Problems via Hadamard Directional Derivative

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Abstract

In this paper, we consider a mathematical program with equilibrium constraints (MPEC) formulated as a mathematical program with complementarity constraints. We obtain necessary conditions of Fritz John (FJ) and Karush-Kuhn-Tucker (KKT) types for a nonsmooth (MPEC) problem in terms of the lower Hadamard directional derivative. In particular sufficient conditions for MPECs are given where the involved functions have pseudoconvex sublevel sets. The functions with pseudoconvex sublevel sets is a class of generalized convex functions that include quasiconvex functions.

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Authors and Affiliations

  1. Department of Mathematics, University of Isfahan, P.O. Box 81745-163, Isfahan, Iran

    A. Ansari Ardali, N. Movahedian & S. Nobakhtian

  2. School of Mathematics, Institute for Research in Fundamental Sciences (IPM), P.O. Box: 19395-5746, Tehran, Iran

    S. Nobakhtian

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  1. A. Ansari Ardali
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  2. N. Movahedian
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  3. S. Nobakhtian
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Correspondence to S. Nobakhtian.

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Ardali, A.A., Movahedian, N. & Nobakhtian, S. Optimality Conditions for Nonsmooth Equilibrium Problems via Hadamard Directional Derivative. Set-Valued Var. Anal 24, 483–497 (2016). https://doi.org/10.1007/s11228-015-0354-3

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  • DOI: https://doi.org/10.1007/s11228-015-0354-3

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