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Mathematical Methods of Operations Research

, Volume 60, Issue 2, pp 331–346 | Cite as

Dual methods for probabilistic optimization problems*

  • Darinka DentchevaEmail author
  • Bogumila Lai
  • Andrzej Ruszczyński
Article

Abstract.

We consider nonlinear stochastic optimization problems with probabilistic constraints. The concept of a p-efficient point of a probability distribution is used to derive equivalent problem formulations, and necessary and sufficient optimality conditions. We analyze the dual functional and its subdifferential. Two numerical methods are developed based on approximations of the p-efficient frontier. The algorithms yield an optimal solution for problems involving r-concave probability distributions. For arbitrary distributions, the algorithms provide upper and lower bounds for the optimal value and nearly optimal solutions. The operation of the methods is illustrated on a cash matching problem with a probabilistic liquidity constraint.

Keywords

Stochastic programming Convex programming Probabilistic constraints Duality Liquidity constraints 

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Copyright information

© Springer-Verlag 2004

Authors and Affiliations

  • Darinka Dentcheva
    • 1
    Email author
  • Bogumila Lai
    • 2
  • Andrzej Ruszczyński
    • 3
  1. 1.Department of MathematicsStevens Institute of TechnologyHobokenUSA
  2. 2.Department of MathematicsStevens Institute of TechnologyHobokenUSA
  3. 3.Department of Management Science and Information SystemsRutgers UniversityPiscatawayU.S.A

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