WIAS Preprint No. 2654, (2019)

Generalized Nash equilibrium problems with partial differential operators: Theory, algorithms, and risk aversion



Authors

  • Gahururu, Deborah
  • Hintermüller, Michael
    ORCID: 0000-0001-9471-2479
  • Stengl, Steven-Marian
  • Surowiec, Thomas M.
    ORCID: 0000-0003-2473-4984

2010 Mathematics Subject Classification

  • 49J20 49J55 49K20 49K45 49M99 65K10 65K15 90C15 91A10

Keywords

  • 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

DOI

10.20347/WIAS.PREPRINT.2654

Abstract

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.

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