Generalized Nash equilibrium problems with partial differential operators: Theory, algorithms, and risk aversion
Generalized Nash equilibrium problems with partial differential operators: Theory, algorithms, and risk aversion
PDE-constrained (generalized) Nash equilibrium problems (GNEPs) are considered in a deterministic setting as well as under uncertainty. This includes a study of deterministic GNEPs with nonlinear and/or multivalued operator equations as forward problems and PDE-constrained GNEPs with uncertain data. The deterministic nonlinear problems are analyzed using the theory of generalized convexity for set-valued operators, and a variational approximation approach is proposed. The stochastic setting includes a detailed overview of the recently developed theory and algorithms for risk-averse PDE-constrained optimization problems. These new results open the way to a rigorous study of stochastic PDE-constrained GNEPs.
- Leibniz Association Germany
- Weierstrass Institute Germany
- Weierstrass Institute for Applied Analysis and Stochastics Germany
ddc:510, fixed-point theory, 65K10, article, 65K15, Generalized Nash equilibrium problems -- PDE-constrained optimization -- L-convexity -- set-valued analysis -- fixed-point theory -- risk averse optimization -- coherent risk measures -- stochastic optimization -- method of multipliers, risk averse optimization, stochastic optimization, 90C15, 510, coherent risk measures, L-convexity, set-valued analysis, 91A10, PDE-constrained optimization, 49J55, 49M99, 49K45, Generalized Nash equilibrium problems, method of multipliers, 49K20, 49J20
ddc:510, fixed-point theory, 65K10, article, 65K15, Generalized Nash equilibrium problems -- PDE-constrained optimization -- L-convexity -- set-valued analysis -- fixed-point theory -- risk averse optimization -- coherent risk measures -- stochastic optimization -- method of multipliers, risk averse optimization, stochastic optimization, 90C15, 510, coherent risk measures, L-convexity, set-valued analysis, 91A10, PDE-constrained optimization, 49J55, 49M99, 49K45, Generalized Nash equilibrium problems, method of multipliers, 49K20, 49J20
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