Stability of solutions for stochastic programs with complete recourse

Stability of solutions for stochastic programs with complete recourse

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Article ID: iaor1994742
Country: United States
Volume: 18
Issue: 3
Start Page Number: 590
End Page Number: 609
Publication Date: Aug 1993
Journal: Mathematics of Operations Research
Authors: ,
Keywords: programming: multiple criteria
Abstract:

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 varies 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 asslmption is given and verified for recourse problems with separable and nonseparable objectives.

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