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

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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.

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Notes

  1. This concept is not the joint convexity of a game as defined by Rosen. In general, they are not comparable, but our assumption is stronger when all players have the same constraint, i.e. \(g_j=g\), for all \(j\in J\).

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Acknowledgements

This research benefited from the support of the FMJH Program Gaspard Monge in optimisation and operation research, and from the support to this program from EDF. The second author was also benefited by a grant CONICYT-PFCHA/Doctorado Nacional/2018 N21180645.

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Authors and Affiliations

  1. University of Perpignan, Lab. PROMES UPR CNRS 8521, Perpignan, France

    Didier Aussel & Anton Svensson

  2. Universidad de Chile, Santiago, Chile

    Anton Svensson

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  1. Didier Aussel
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  2. Anton Svensson
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Correspondence to Didier Aussel.

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Aussel, D., Svensson, A. Towards Tractable Constraint Qualifications for Parametric Optimisation Problems and Applications to Generalised Nash Games. J Optim Theory Appl 182, 404–416 (2019). https://doi.org/10.1007/s10957-019-01529-4

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  • DOI: https://doi.org/10.1007/s10957-019-01529-4

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