Dual methods for probabilistic optimization problems *

Darinka Dentcheva, Bogumila Lai and Andrzej Ruszczynski ()

Mathematical Methods of Operations Research, 2004, vol. 60, issue 2, 346 pages

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. Copyright Springer-Verlag 2004

Keywords: Stochastic programming; Convex programming; Probabilistic constraints; Duality; Liquidity constraints (search for similar items in EconPapers)
Date: 2004
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Persistent link: https://EconPapers.repec.org/RePEc:spr:mathme:v:60:y:2004:i:2:p:331-346

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DOI: 10.1007/s001860400371

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