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Stability and Sensitivity of Optimization Problems with First Order Stochastic Dominance Constraints

Please always quote using this URN:urn:nbn:de:0296-matheon-3822
  • We analyze the stability and sensitivity of stochastic optimization problems with stochastic dominance constraints of first order. We consider general perturbations of the underlying probability measures in the space of regular measures equipped with a suitable discrepancy distance. We show that the graph of the feasible set mapping is closed under rather general assumptions. We obtain conditions for the continuity of the optimal value and upper-semicontinuity of the optimal solutions, as well as quantitative stability estimates of Lipschitz type. Furthermore, we analyze the sensitivity of the optimal value and obtain upper and lower bounds for the directional derivatives of the optimal value. The estimates are formulated in terms of the dual utility functions associated with the dominance constraints.

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Metadaten
Author:Darinka Dentcheva, Rene Henrion, Andrzej Ruszczynski
URN:urn:nbn:de:0296-matheon-3822
Referee:Peter Imkeller
Document Type:Preprint, Research Center Matheon
Language:English
Date of first Publication:2007/04/04
Release Date:2007/03/29
Tag:
Institute:Humboldt-Universität zu Berlin
Weierstraß-Institut für Angewandte Analysis und Stochastik (WIAS)
MSC-Classification:46-XX FUNCTIONAL ANALYSIS (For manifolds modeled on topological linear spaces, see 57Nxx, 58Bxx) / 46Nxx Miscellaneous applications of functional analysis [See also 47Nxx] / 46N10 Applications in optimization, convex analysis, mathematical programming, economics
60-XX PROBABILITY THEORY AND STOCHASTIC PROCESSES (For additional applications, see 11Kxx, 62-XX, 90-XX, 91-XX, 92-XX, 93-XX, 94-XX) / 60Exx Distribution theory [See also 62Exx, 62Hxx] / 60E15 Inequalities; stochastic orderings
90-XX OPERATIONS RESEARCH, MATHEMATICAL PROGRAMMING / 90Cxx Mathematical programming [See also 49Mxx, 65Kxx] / 90C15 Stochastic programming
90-XX OPERATIONS RESEARCH, MATHEMATICAL PROGRAMMING / 90Cxx Mathematical programming [See also 49Mxx, 65Kxx] / 90C34 Semi-infinite programming
90-XX OPERATIONS RESEARCH, MATHEMATICAL PROGRAMMING / 90Cxx Mathematical programming [See also 49Mxx, 65Kxx] / 90C48 Programming in abstract spaces
91-XX GAME THEORY, ECONOMICS, SOCIAL AND BEHAVIORAL SCIENCES / 91Bxx Mathematical economics (For econometrics, see 62P20) / 91B06 Decision theory [See also 62Cxx, 90B50, 91A35]
Preprint Number:381
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