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Optimization and equilibrium problems with equilibrium constraints

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  • Mordukhovich, Boris S.

Abstract

This paper concerns optimization and equilibrium problems with the so-called equilibrium constraints mathematical programs with equilibrium constraint (MPEC) and equilibrium problems with equilibrium constraint (EPEC), which frequently appear in applications to operations research. These classes of problems can be naturally unified in the framework of multiobjective optimization with constraints governed by parametric variational systems (generalized equations, variational inequalities, complementarity problems, etc.). We focus on necessary conditions for optimal solutions to MPECs and EPECs under general assumptions in finite-dimensional spaces. Since such problems are intrinsically nonsmooth, we use advanced tools of generalized differentiation to study optimal solutions by methods of modern variational analysis. The general results obtained are concretized for special classes of MPECs and EPECs important in applications.

Suggested Citation

  • Mordukhovich, Boris S., 2005. "Optimization and equilibrium problems with equilibrium constraints," Omega, Elsevier, vol. 33(5), pages 379-384, October.
    • Handle: RePEc:eee:jomega:v:33:y:2005:i:5:p:379-384
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    Cited by:

    1. P. Q. Khanh & N. D. Tuan, 2007. "Optimality Conditions for Nonsmooth Multiobjective Optimization Using Hadamard Directional Derivatives," Journal of Optimization Theory and Applications, Springer, vol. 133(3), pages 341-357, June.
    2. Watling, D.P. & Shepherd, S.P. & Koh, A., 2015. "Cordon toll competition in a network of two cities: Formulation and sensitivity to traveller route and demand responses," Transportation Research Part B: Methodological, Elsevier, vol. 76(C), pages 93-116.
    3. Acuna, Jorge A. & Zayas-Castro, Jose L. & Feijoo, Felipe, 2022. "A bilevel Nash-in-Nash model for hospital mergers: A key to affordable care," Socio-Economic Planning Sciences, Elsevier, vol. 83(C).
    4. Gühnemann, Astrid & Koh, Andrew & Shepherd, Simon & Lawler, Mary, 2011. "Implications of interdependencies between charging strategies of local authorities for the protection of sensitive areas in the Trans-Pennine Corridor," Utilities Policy, Elsevier, vol. 19(1), pages 42-52, January.
    5. Feijoo, Felipe & Das, Tapas K., 2014. "Design of Pareto optimal CO2 cap-and-trade policies for deregulated electricity networks," Applied Energy, Elsevier, vol. 119(C), pages 371-383.

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