TY - JOUR
T1 - Semi-infinite probabilistic optimization
T2 - First-order stochastic dominance constrain
AU - Dentcheva, Darinka
AU - Ruszczyński, Andrzej
PY - 2004/10
Y1 - 2004/10
N2 - We consider stochastic optimization problems involving a continuum of probabilistic constraints. They are equivalent to stochastic dominance constraints of first order, frequently called stochastic ordering constraints. We develop necessary and sufficient conditions of optimality for these models. We show that the Lagrange multipliers corresponding to dominance constraints can be identified with piecewise constant nondecreasing utility functions. We also show that the convexification of stochastic ordering relation is equivalent to second-order stochastic dominance under rather weak assumptions.
AB - We consider stochastic optimization problems involving a continuum of probabilistic constraints. They are equivalent to stochastic dominance constraints of first order, frequently called stochastic ordering constraints. We develop necessary and sufficient conditions of optimality for these models. We show that the Lagrange multipliers corresponding to dominance constraints can be identified with piecewise constant nondecreasing utility functions. We also show that the convexification of stochastic ordering relation is equivalent to second-order stochastic dominance under rather weak assumptions.
KW - Chance constraints
KW - Convexification
KW - Duality
KW - Generalized concavity
KW - Risk
KW - Semi-infinite optimization
KW - Stochastic ordering
KW - Stochastic programming
UR - http://www.scopus.com/inward/record.url?scp=13244269988&partnerID=8YFLogxK
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U2 - 10.1080/02331930412331327148
DO - 10.1080/02331930412331327148
M3 - Article
AN - SCOPUS:13244269988
SN - 0233-1934
VL - 53
SP - 583
EP - 601
JO - Optimization
JF - Optimization
IS - 5-6
ER -