TY - JOUR
T1 - Dual methods for probabilistic optimization problems
AU - Dentcheva, Darinka
AU - Lai, Bogumila
AU - Ruszczyński, Andrzej
PY - 2004/10
Y1 - 2004/10
N2 - 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.
AB - 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.
KW - Convex programming
KW - Duality
KW - Liquidity constraints
KW - Probabilistic constraints
KW - Stochastic programming
UR - http://www.scopus.com/inward/record.url?scp=10044255579&partnerID=8YFLogxK
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U2 - 10.1007/s001860400371
DO - 10.1007/s001860400371
M3 - Article
AN - SCOPUS:10044255579
SN - 1432-2994
VL - 60
SP - 331
EP - 346
JO - Mathematical Methods of Operations Research
JF - Mathematical Methods of Operations Research
IS - 2
ER -