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SPEPS Preprint

Author(s): Darinka Dentcheva, Stevens Institute of Technology
Bogumila Lai, Stevens Institute of Technology
Andrzej Ruszczynski, Rutgers University
Title: Efficient point methods for probabilistic optimization problems
Date of Acceptance: 20.10.2003
Submission Date: 10.08.2003
Series Title: Stochastic Programming E-Print Series
(SPEPS)
Editors: Julie L. Higle; Werner Römisch; Surrajeet Sen
Keywords (eng): Stochastic Programming, Convex Programming, Probabilistic Constraints, Dual Methods
Appeared in: Mathematical methods of operations research 2 (Vol. 60, 2004)
Springer (Berlin [u.a.])
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Abstract (eng):
We consider nonlinear stochastic programming 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.
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  • PDF – 375 (10.71 pro Monat)
 
 
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