Regular Selections of Multifunctions and Random Sets - Dentcheva, Darinka
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The methodology presented in this work yields existence of selections and Castaing representations of these sets that enjoy stability properties. Particularly, work on differential stability of solution sets of two-stage stochastic optimization problems is presented. We identify conditions such that the optimal value function has first- and second-order directional derivatives and the solution-set mapping is directionally differentiable into admissible directions. Moreover, the form of the semi-derivative is identified, and we have given a formula for it. The sensitivity analysis is carried…mehr

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Produktbeschreibung
The methodology presented in this work yields existence of selections and Castaing representations of these sets that enjoy stability properties. Particularly, work on differential stability of solution sets of two-stage stochastic optimization problems is presented. We identify conditions such that the optimal value function has first- and second-order directional derivatives and the solution-set mapping is directionally differentiable into admissible directions. Moreover, the form of the semi-derivative is identified, and we have given a formula for it. The sensitivity analysis is carried out by exploiting structural properties of the optimization model. We obtain differentiability properties of solution sets and extend earlier results on directional differentiability of optimal values considerably.
Autorenporträt
Darinka Dentcheva is a Bulgarian-American mathematician, noted for her contributions to convex analysis, stochastic programming, and risk-averse optimization. She developed the theory of Steiner selections of multifunctions, the theory of stochastic dominance constraints, and contributed to the theory of unit commitment in power systems.