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Optimality conditions and duality for semi-infinite mathematical programming problems with equilibrium constraints, using convexificators

Author

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  • Yogendra Pandey

    (Indian Institute of Technology)

  • S. K. Mishra

    (Banaras Hindu University)

Abstract

In this paper, we consider semi-infinite mathematical programming problems with equilibrium constraints (SIMPEC). We establish necessary and sufficient optimality conditions for the SIMPEC, using convexificators. We study the Wolfe type dual problem for the SIMPEC under the $$\partial ^{*}$$ ∂ ∗ -convexity assumption. A Mond–Weir type dual problem is also formulated and studied for the SIMPEC under the $$\partial ^{*}$$ ∂ ∗ -convexity, $$\partial ^{*}$$ ∂ ∗ -pseudoconvexity and $$\partial ^{*}$$ ∂ ∗ -quasiconvexity assumptions. Weak duality theorems are established to relate the SIMPEC and two dual programs in the framework of convexificators. Further, strong duality theorems are obtained under generalized standard Abadie constraint qualification.

Suggested Citation

  • Yogendra Pandey & S. K. Mishra, 2018. "Optimality conditions and duality for semi-infinite mathematical programming problems with equilibrium constraints, using convexificators," Annals of Operations Research, Springer, vol. 269(1), pages 549-564, October.
    • Handle: RePEc:spr:annopr:v:269:y:2018:i:1:d:10.1007_s10479-017-2422-6
    DOI: 10.1007/s10479-017-2422-6
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    References listed on IDEAS

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