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Equilibrium Constrained Optimization Problems

Author

Listed:
  • Birbil, S.I.
  • Bouza, G.
  • Frenk, J.B.G.
  • Still, G.J.

Abstract

We consider equilibrium constrained optimization problems, which have a general formulationthat encompasses well-known models such as mathematical programs with equilibrium constraints, bilevel programs, and generalized semi-infinite programming problems. Based on the celebrated K K M lemma, we prove the existence of feasible points for the equilibrium constraints. Moreover, we analyze the topological and analytical structure of the feasible set. Alternative formulations of an equilibrium constrained optimization problem (ECOP) that are suitable for numerical purposes are also given. As an important _rst step for developing ef_cient algorithms, we provide a genericity analysis for the feasible set of a particular ECOP, for which all the functions are assumed to be linear.

Suggested Citation

  • Birbil, S.I. & Bouza, G. & Frenk, J.B.G. & Still, G.J., 2003. "Equilibrium Constrained Optimization Problems," Econometric Institute Research Papers ERS-2003-085-LIS, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    • Handle: RePEc:ems:eureir:1068
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    References listed on IDEAS

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    1. Holger Scheel & Stefan Scholtes, 2000. "Mathematical Programs with Complementarity Constraints: Stationarity, Optimality, and Sensitivity," Mathematics of Operations Research, INFORMS, vol. 25(1), pages 1-22, February.
    2. Still, G., 1999. "Generalized semi-infinite programming: Theory and methods," European Journal of Operational Research, Elsevier, vol. 119(2), pages 301-313, December.
    3. Georg Still, 2002. "Linear bilevel problems: Genericity results and an efficient method for computing local minima," The Annals of Regional Science, Springer;Western Regional Science Association, vol. 55(3), pages 383-400, June.
    4. Georg Still, 2002. "Linear bilevel problems: Genericity results and an efficient method for computing local minima," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 55(3), pages 383-400, June.
    5. Yang, Z.F., 1996. "Simplicial fixed point algorithms and applications," Other publications TiSEM 60fbb5f7-785c-4c91-8b84-5, Tilburg University, School of Economics and Management.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    bilevel programs; equilibrium problems; existence; generalized semi-infinite programming; genericity; mathematical programs with equilibrium constraints; problems with complementarity constraints;
    All these keywords.

    JEL classification:

    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • M - Business Administration and Business Economics; Marketing; Accounting; Personnel Economics
    • M11 - Business Administration and Business Economics; Marketing; Accounting; Personnel Economics - - Business Administration - - - Production Management
    • R4 - Urban, Rural, Regional, Real Estate, and Transportation Economics - - Transportation Economics

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