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Stability of solutions for stochastic programs with complete recourse. (English) Zbl 0797.90070
Quantitative continuity of optimal solution sets to convex stochastic programs with (linear) complete recourse and random right-hand sides is investigated when the underlying probability measure various in a metric space. The central result asserts that, under a strong convexity condition for the expected recourse in the unperturbed problem, optimal tenders behave Hölder-continuous with respect to a Wasserstein metric. For linear stochastic programs this carries over to the Hausdorff distance of optimal solution sets. A general sufficient condition for the crucial strong-convexity assumption is given and verified for recourse problems with separable and nonseparable objectives.

90C15 Stochastic programming
90C31 Sensitivity, stability, parametric optimization
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