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Regular Selections of Multifunctions and Random Sets

Regular Selections of Multifunctions and Random Setsaf Darinka Dentcheva
Bag om Regular Selections of Multifunctions and Random Sets

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.

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  • Sprog:
  • Engelsk
  • ISBN:
  • 9783659801242
  • Indbinding:
  • Paperback
  • Sideantal:
  • 132
  • Udgivet:
  • 2. november 2018
  • Størrelse:
  • 150x8x220 mm.
  • Vægt:
  • 215 g.
  • 2-3 uger.
  • 26. november 2024
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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 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.

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