Stability of solutions for stochastic programs with complete recourse

作者: Werner Römisch , Rüdiger Schultz

DOI: 10.1287/MOOR.18.3.590

关键词:

摘要: 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 strong-convexity condition for expected unperturbed problem, tenders behave Holder-continuous respect Wasserstein metric. For linear this carries over Hausdorff distance A general sufficient crucial assumption given verified problems separable nonseparable objectives.

参考文章(26)
Matthias Gelbrich, On a Formula for the L2 Wasserstein Metric between Measures on Euclidean and Hilbert Spaces Mathematische Nachrichten. ,vol. 147, pp. 185- 203 ,(1990) , 10.1002/MANA.19901470121
P. Kall, A. Ruszczyński, K. Frauendorfer, Approximation Techniques in Stochastic Programming Springer Berlin Heidelberg. pp. 33- 64 ,(1988) , 10.1007/978-3-642-61370-8_2
Patrick Billingsley, Convergence of Probability Measures ,(1968)
B. (Bernd) Bank, Non-linear parametric optimization ,(1983)
John R. Birge, Roger J.-B. Wets, Designing approximation schemes for stochastic optimization problems, in particular for stochastic programs with recourse Mathematical Programming Studies. ,vol. 27, pp. 54- 102 ,(1986) , 10.1007/BFB0121114
W. Römisch, A. Wakolbinger, Obtaining convergence rates for approximations in stochastic programming Mathematical research. ,vol. 35, pp. 327- 343 ,(1987)
Frank H. Clarke, Optimization and nonsmooth analysis ,(1983)
Peter Kall, János Mayer, Stochastic Linear Programming ,(1975)
Roger J.-B. Wets, Stochastic Programs with Fixed Recourse: The Equivalent Deterministic Program SIAM Review. ,vol. 16, pp. 309- 339 ,(1974) , 10.1137/1016053