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

  • Didier AusselEmail author
  • Anton Svensson


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.


Parametric optimisation Constraint qualifications KKT conditions GNEP Joint convexity 

Mathematics Subject Classification

90C31 90C33 90C46 91A40 



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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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.University of Perpignan, Lab. PROMES UPR CNRS 8521PerpignanFrance
  2. 2.Universidad de ChileSantiagoChile

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