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Risk-Neutral PDE-Constrained Generalized Nash Equilibrium Problems

Submission Status:revision under review
  • A class of risk-neutral PDE-constrained generalized Nash equilibrium problems is introduced in which the feasible strategy set of each player is subject to a common linear elliptic partial differential equation with random inputs. In addition, each player’s actions are taken from a bounded, closed, and convex set on the individual strategies and a bound constraint on the common state variable. Existence of Nash equilibria and first-order optimality conditions are derived by exploiting higher integrability and regularity of the random field state variables and a specially tailored constraint qualification for GNEPs with the assumed structure. A relaxation scheme based on the Moreau-Yosida approximation of the bound constraint is proposed, which ultimately leads to numerical algorithms for the individual player problems as well as the GNEP as a whole. The relaxation scheme is related to probability constraints and the viability of the proposed numerical algorithms are demonstrated via several examples.

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Author:Deborah Gahururu, Michael Hintermüller, Thomas Surowiec
Document Type:Preprint
Language:English
Date of Publication (online):2021/02/02
Date of first Publication:2021/10/18
Release Date:2021/10/18
Institutes:Humboldt-Universität zu Berlin
Weierstraß-Institut für Angewandte Analysis und Stochastik
Subprojects:B02
Licence (German):License LogoCreative Commons - CC BY - Namensnennung 4.0 International