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New Sharp Necessary Optimality Conditions for Mathematical Programs with Equilibrium Constraints

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Abstract

In this paper, we study the mathematical program with equilibrium constraints formulated as a mathematical program with a parametric generalized equation involving the regular normal cone. We derive a new necessary optimality condition which is sharper than the usual M-stationary condition and is applicable even when no constraint qualifications hold for the corresponding mathematical program with complementarity constraints reformulation.

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Acknowledgments

The research of H. Gfrerer was partially supported by the Austrian Science Fund (FWF) under grant P29190-N32. The research of J.J. Ye was partially supported by NSERC.

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Authors and Affiliations

  1. Institute of Computational Mathematics, Johannes Kepler University Linz, A-4040, Linz, Austria

    Helmut Gfrerer

  2. Department of Mathematics and Statistics, University of Victoria, Victoria, B.C., V8W 2Y2, Canada

    Jane J. Ye

Authors
  1. Helmut Gfrerer
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  2. Jane J. Ye
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Correspondence to Helmut Gfrerer.

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Gfrerer, H., Ye, J.J. New Sharp Necessary Optimality Conditions for Mathematical Programs with Equilibrium Constraints. Set-Valued Var. Anal 28, 395–426 (2020). https://doi.org/10.1007/s11228-019-00519-y

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