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

Didier Aussel () and Anton Svensson ()
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Didier Aussel: University of Perpignan, Lab. PROMES UPR CNRS 8521
Anton Svensson: University of Perpignan, Lab. PROMES UPR CNRS 8521

Journal of Optimization Theory and Applications, 2019, vol. 182, issue 1, No 17, 404-416

Abstract: 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.

Keywords: Parametric optimisation; Constraint qualifications; KKT conditions; GNEP; Joint convexity; 90C31; 90C33; 90C46; 91A40 (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (5)

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DOI: 10.1007/s10957-019-01529-4

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