TY - JOUR
T1 - Concavity and efficient points of discrete distributions in probabilistic programming
AU - Dentcheva, Darinka
AU - Prékopa, András
AU - Ruszczyński, Andrzej
PY - 2000
Y1 - 2000
N2 - We consider stochastic programming problems with probabilistic constraints involving integer-valued random variables. The concept of a p-efficient point of a probability distribution is used to derive various equivalent problem formulations. Next we introduce the concept of r-concave discrete probability distributions and analyse its relevance for problems under consideration. These notions are used to derive lower and upper bounds for the optimal value of probabilistically constrained stochastic programming problems with discrete random variables. The results are illustrated with numerical examples.
AB - We consider stochastic programming problems with probabilistic constraints involving integer-valued random variables. The concept of a p-efficient point of a probability distribution is used to derive various equivalent problem formulations. Next we introduce the concept of r-concave discrete probability distributions and analyse its relevance for problems under consideration. These notions are used to derive lower and upper bounds for the optimal value of probabilistically constrained stochastic programming problems with discrete random variables. The results are illustrated with numerical examples.
KW - Column generation
KW - Discrete distributions
KW - Generalized concavity
KW - Probabilistic programming
UR - http://www.scopus.com/inward/record.url?scp=0001958747&partnerID=8YFLogxK
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U2 - 10.1007/PL00011393
DO - 10.1007/PL00011393
M3 - Article
AN - SCOPUS:0001958747
SN - 0025-5610
VL - 89
SP - 55
EP - 77
JO - Mathematical Programming
JF - Mathematical Programming
IS - 1
ER -