TY - JOUR
T1 - Stability and sensitivity of optimization problems with first order stochastic dominance constraints
AU - Dentcheva, Darinka
AU - Henrion, René
AU - Ruszczyński, Andrzej
PY - 2007
Y1 - 2007
N2 - We analyze the stability and sensitivity of stochastic optimization problems with stochastic dominance constraints of first order. We consider general perturbations of the underlying probability measures in the space of regular measures equipped with a suitable discrepancy distance. We show that the graph of the feasible set mapping is closed under rather general assumptions. We obtain conditions for the continuity of the optimal value and upper-semicontinuity of the optimal solutions, as well as quantitative stability estimates of Lipschitz type. Furthermore, we analyze the sensitivity of the optimal value and obtain upper and lower bounds for the directional derivatives of the optimal value. The estimates are formulated in terms of the dual utility functions associated with the dominance constraints.
AB - We analyze the stability and sensitivity of stochastic optimization problems with stochastic dominance constraints of first order. We consider general perturbations of the underlying probability measures in the space of regular measures equipped with a suitable discrepancy distance. We show that the graph of the feasible set mapping is closed under rather general assumptions. We obtain conditions for the continuity of the optimal value and upper-semicontinuity of the optimal solutions, as well as quantitative stability estimates of Lipschitz type. Furthermore, we analyze the sensitivity of the optimal value and obtain upper and lower bounds for the directional derivatives of the optimal value. The estimates are formulated in terms of the dual utility functions associated with the dominance constraints.
KW - Chance constraints
KW - Directional differentiability
KW - Lipschitz stability
KW - Metric regularity
KW - Semi-infinite optimization
KW - Stochastic ordering
KW - Stochastic programming
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U2 - 10.1137/060650118
DO - 10.1137/060650118
M3 - Article
AN - SCOPUS:39449105136
SN - 1052-6234
VL - 18
SP - 322
EP - 337
JO - SIAM Journal on Optimization
JF - SIAM Journal on Optimization
IS - 1
ER -