A pessimistic bilevel stochastic problem for elastic shape optimization

We consider pessimistic bilevel stochastic programs in which the follower maximizes over a fixed compact convex set strictly quadratic function, whose Hessian depends on leader's decision. The resulting random variable is evaluated by risk measure. Under assumptions including real analyticity of lower-level goal we prove existence optimal solutions. discuss an alternate model where leader hedges against solutions, and show that this case solvability can be guaranteed under weaker conditions both deterministic setting. approach applied to mechanical shape optimization problem decides material distribution minimize tracking-type cost functional, whereas chooses forces from admissible maximize compliance objective. considered stochastically perturbed actual construction phase. Computational results illustrate concept demonstrate interplay design testing.