WIAS Preprint No. 2962, (2022)

Risk-averse optimal control of random elliptic VIs


  • Alphonse, Amal
    ORCID: 0000-0001-7616-3293
  • Geiersbach, Caroline
    ORCID: 0000-0002-6518-7756
  • Hintermüller, Michael
    ORCID: 0000-0001-9471-2479
  • Surowiec, Thomas M.
    ORCID: 0000-0003-2473-4984

2020 Mathematics Subject Classification

  • 49J20 49J55 49K20 90C15 49K45


  • Stochastic mathematical programs with equilibrium constraints, constrained optimal control, elliptic variational inequalities under uncertainty, stochastic optimisation, risk measures




We consider a risk-averse optimal control problem governed by an elliptic variational inequality (VI) subject to random inputs. By deriving KKT-type optimality conditions for a penalised and smoothed problem and studying convergence of the stationary points with respect to the penalisation parameter, we obtain two forms of stationarity conditions. The lack of regularity with respect to the uncertain parameters and complexities induced by the presence of the risk measure give rise to new challenges unique to the stochastic setting. We also propose a path-following stochastic approximation algorithm using variance reduction techniques and demonstrate the algorithm on a modified benchmark problem.

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