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Two-stage stochastic optimization problems with stochastic ordering constraints on the recourse

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  • Dentcheva, Darinka
  • Martinez, Gabriela

Abstract

We consider two-stage risk-averse stochastic optimization problems with a stochastic ordering constraint on the recourse function. Two new characterizations of the increasing convex order relation are provided. They are based on conditional expectations and on integrated quantile functions: a counterpart of the Lorenz function. We propose two decomposition methods to solve the problems and prove their convergence. Our methods exploit the decomposition structure of the risk-neutral two-stage problems and construct successive approximations of the stochastic ordering constraints. Numerical results confirm the efficiency of the methods.

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File URL: http://www.sciencedirect.com/science/article/pii/S0377221711010538
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Bibliographic Info

Article provided by Elsevier in its journal European Journal of Operational Research.

Volume (Year): 219 (2012)
Issue (Month): 1 ()
Pages: 1-8

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Handle: RePEc:eee:ejores:v:219:y:2012:i:1:p:1-8

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Web page: http://www.elsevier.com/locate/eor

Related research

Keywords: Increasing convex order; Stochastic dominance; Decomposition methods; Lorenz curve; Survival function; Stochastic programming;

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Cited by:
  1. Wim Ackooij & Welington Oliveira, 2014. "Level bundle methods for constrained convex optimization with various oracles," Computational Optimization and Applications, Springer, vol. 57(3), pages 555-597, April.
  2. Wang, S. & Huang, G.H., 2014. "An integrated approach for water resources decision making under interactive and compound uncertainties," Omega, Elsevier, vol. 44(C), pages 32-40.
  3. Alonso-Ayuso, Antonio & Carvallo, Felipe & Escudero, Laureano F. & Guignard, Monique & Pi, Jiaxing & Puranmalka, Raghav & Weintraub, Andrés, 2014. "Medium range optimization of copper extraction planning under uncertainty in future copper prices," European Journal of Operational Research, Elsevier, vol. 233(3), pages 711-726.

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