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Analysis of a New Sequential Optimality Condition Applied to Mathematical Programs with Equilibrium Constraints

Author

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  • Elias S. Helou

    (University of São Paulo)

  • Sandra A. Santos

    (University of Campinas)

  • Lucas E. A. Simões

    (University of Campinas)

Abstract

In this study, a novel sequential optimality condition for general continuous optimization problems is established. In the context of mathematical programs with equilibrium constraints, the condition is proved to ensure Clarke stationarity. Originally devised for constrained nonsmooth optimization, the proposed sequential optimality condition addresses the domain of the constraints instead of their images, capturing indistinctly the features of the complementarity and the ordinary constraints of optimization problems modeling equilibrium conditions.

Suggested Citation

  • Elias S. Helou & Sandra A. Santos & Lucas E. A. Simões, 2020. "Analysis of a New Sequential Optimality Condition Applied to Mathematical Programs with Equilibrium Constraints," Journal of Optimization Theory and Applications, Springer, vol. 185(2), pages 433-447, May.
    • Handle: RePEc:spr:joptap:v:185:y:2020:i:2:d:10.1007_s10957-020-01658-1
    DOI: 10.1007/s10957-020-01658-1
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    References listed on IDEAS

    as
    1. J. V. Outrata, 1999. "Optimality Conditions for a Class of Mathematical Programs with Equilibrium Constraints," Mathematics of Operations Research, INFORMS, vol. 24(3), pages 627-644, August.
    2. Joydeep Dutta & Kalyanmoy Deb & Rupesh Tulshyan & Ramnik Arora, 2013. "Approximate KKT points and a proximity measure for termination," Journal of Global Optimization, Springer, vol. 56(4), pages 1463-1499, August.
    3. Didier Aussel & Anton Svensson, 2019. "Is Pessimistic Bilevel Programming a Special Case of a Mathematical Program with Complementarity Constraints?," Journal of Optimization Theory and Applications, Springer, vol. 181(2), pages 504-520, May.
    4. 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.
    5. Bard, Jonathan F. & Plummer, John & Claude Sourie, Jean, 2000. "A bilevel programming approach to determining tax credits for biofuel production," European Journal of Operational Research, Elsevier, vol. 120(1), pages 30-46, January.
    6. Benoît Colson & Patrice Marcotte & Gilles Savard, 2007. "An overview of bilevel optimization," Annals of Operations Research, Springer, vol. 153(1), pages 235-256, September.
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    Cited by:

    1. Ademir A. Ribeiro & Mael Sachine & Evelin H. M. Krulikovski, 2022. "A Comparative Study of Sequential Optimality Conditions for Mathematical Programs with Cardinality Constraints," Journal of Optimization Theory and Applications, Springer, vol. 192(3), pages 1067-1083, March.
    2. Renan W. Prado & Sandra A. Santos & Lucas E. A. Simões, 2023. "On the Fulfillment of the Complementary Approximate Karush–Kuhn–Tucker Conditions and Algorithmic Applications," Journal of Optimization Theory and Applications, Springer, vol. 197(2), pages 705-736, May.

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