TY - JOUR
T1 - Two-stage stochastic optimization problems with stochastic ordering constraints on the recourse
AU - Dentcheva, Darinka
AU - Martinez, Gabriela
PY - 2012/5/16
Y1 - 2012/5/16
N2 - We consider two-stage risk-averse stochastic optimization problems with a stochastic ordering constraint on the recourse function. Two new characterizations of the increasing convex order relation are provided. They are based on conditional expectations and on integrated quantile functions: a counterpart of the Lorenz function. We propose two decomposition methods to solve the problems and prove their convergence. Our methods exploit the decomposition structure of the risk-neutral two-stage problems and construct successive approximations of the stochastic ordering constraints. Numerical results confirm the efficiency of the methods.
AB - We consider two-stage risk-averse stochastic optimization problems with a stochastic ordering constraint on the recourse function. Two new characterizations of the increasing convex order relation are provided. They are based on conditional expectations and on integrated quantile functions: a counterpart of the Lorenz function. We propose two decomposition methods to solve the problems and prove their convergence. Our methods exploit the decomposition structure of the risk-neutral two-stage problems and construct successive approximations of the stochastic ordering constraints. Numerical results confirm the efficiency of the methods.
KW - Decomposition methods
KW - Increasing convex order
KW - Lorenz curve
KW - Stochastic dominance
KW - Stochastic programming
KW - Survival function
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U2 - 10.1016/j.ejor.2011.11.044
DO - 10.1016/j.ejor.2011.11.044
M3 - Article
AN - SCOPUS:84856532757
SN - 0377-2217
VL - 219
SP - 1
EP - 8
JO - European Journal of Operational Research
JF - European Journal of Operational Research
IS - 1
ER -