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Towards Tractable Constraint Qualifications for Parametric Optimisation Problems and Applications to Generalised Nash Games

Author

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  • Didier Aussel

    (University of Perpignan, Lab. PROMES UPR CNRS 8521)

  • Anton Svensson

    (University of Perpignan, Lab. PROMES UPR CNRS 8521
    Universidad de Chile)

Abstract

A generalised Nash game is a non-cooperative game in which each player is facing an optimisation problem where both the objective function and the feasible set depend on the variables of the other players. A classical way to treat numerically this difficult problem is to solve the nonlinear system composed of the concatenation of the Karush–Kuhn–Tucker optimality conditions of each player’s problem. The aim of this work is to provide constraint qualification conditions ensuring that both problems share the same set of solutions. Our main target here is to elaborate tractable conditions, that is, sets of conditions that are as simple as possible to fulfil. This is achieved through the analysis of “minimal” qualification conditions for parametric optimisation problems.

Suggested Citation

  • Didier Aussel & Anton Svensson, 2019. "Towards Tractable Constraint Qualifications for Parametric Optimisation Problems and Applications to Generalised Nash Games," Journal of Optimization Theory and Applications, Springer, vol. 182(1), pages 404-416, July.
    • Handle: RePEc:spr:joptap:v:182:y:2019:i:1:d:10.1007_s10957-019-01529-4
    DOI: 10.1007/s10957-019-01529-4
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    References listed on IDEAS

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    1. Stein, Oliver & Sudermann-Merx, Nathan, 2018. "The noncooperative transportation problem and linear generalized Nash games," European Journal of Operational Research, Elsevier, vol. 266(2), pages 543-553.
    2. Axel Dreves, 2017. "Computing all solutions of linear generalized Nash equilibrium problems," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 85(2), pages 207-221, April.
    3. E. G. Birgin & G. Haeser & A. Ramos, 2018. "Augmented Lagrangians with constrained subproblems and convergence to second-order stationary points," Computational Optimization and Applications, Springer, vol. 69(1), pages 51-75, January.
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    Cited by:

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    2. Xi, Haoning & Aussel, Didier & Liu, Wei & Waller, S.Travis. & Rey, David, 2024. "Single-leader multi-follower games for the regulation of two-sided mobility-as-a-service markets," European Journal of Operational Research, Elsevier, vol. 317(3), pages 718-736.
    3. Aussel, Didier & Cao Van, Kien & Salas, David, 2023. "Optimal design of exchange water networks with control inputs in Eco-Industrial Parks," Energy Economics, Elsevier, vol. 120(C).
    4. Tiago Roux Oliveira & Victor Hugo Pereira Rodrigues & Miroslav Krstić & Tamer Başar, 2021. "Nash Equilibrium Seeking in Quadratic Noncooperative Games Under Two Delayed Information-Sharing Schemes," Journal of Optimization Theory and Applications, Springer, vol. 191(2), pages 700-735, December.

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