Jointly Convex Generalized Nash Equilibria and Elliptic Multiobjective Optimal Control

Axel Dreves () and Joachim Gwinner ()
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Axel Dreves: Universität der Bundeswehr München
Joachim Gwinner: Universität der Bundeswehr München

Journal of Optimization Theory and Applications, 2016, vol. 168, issue 3, No 19, 1065-1086

Abstract: Abstract We deal with jointly convex generalized Nash equilibrium problems in infinite-dimensional spaces. For their solution, we extend a finite-dimensional optimization approach and design a convergent algorithm in Hilbert space. Then we apply our investigations to a class of multiobjective optimal control problems with control and state constraints that are governed by elliptic partial differential equations. We present a new reformulation as a jointly convex generalized Nash equilibrium problem. We study a finite element approximation of such a multiobjective optimal control problem, and further we prove convergence in appropriate function spaces. Finally, we provide some numerical results that show the effectiveness of our algorithm for multiobjective optimal control problems.

Keywords: Jointly convex generalized Nash equilibrium problem; Normalized Nash equilibrium; Multiobjective optimal control; Elliptic partial differential equation; Control box constraints; State constraints; 49M20; 65N12; 91A10 (search for similar items in EconPapers)
Date: 2016
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DOI: 10.1007/s10957-015-0788-7

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