TY - JOUR
T1 - Augmented Lagrangian method for probabilistic optimization
AU - Dentcheva, Darinka
AU - Martinez, Gabriela
PY - 2012/11
Y1 - 2012/11
N2 - We analyze nonlinear stochastic optimization problems with probabilistic constraints described by continuously differentiable non-convex functions. We describe the tangent and the normal cone to the level sets of the underlying probability function and provide new insight into their structure. Furthermore, we formulate fist order and second order conditions of optimality for these problems based on the notion of p-efficient points. We develop an augmented Lagrangian method for the case of discrete distribution functions. The method is based on progressive inner approximation of the level set of the probability function by generation of p-efficient points. Numerical experience is provided.
AB - We analyze nonlinear stochastic optimization problems with probabilistic constraints described by continuously differentiable non-convex functions. We describe the tangent and the normal cone to the level sets of the underlying probability function and provide new insight into their structure. Furthermore, we formulate fist order and second order conditions of optimality for these problems based on the notion of p-efficient points. We develop an augmented Lagrangian method for the case of discrete distribution functions. The method is based on progressive inner approximation of the level set of the probability function by generation of p-efficient points. Numerical experience is provided.
KW - Chance constraints
KW - Probabilistic constraints
KW - Second-order optimality conditions
KW - Stochastic programming
KW - p-efficient points
UR - http://www.scopus.com/inward/record.url?scp=84867399267&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84867399267&partnerID=8YFLogxK
U2 - 10.1007/s10479-011-0884-5
DO - 10.1007/s10479-011-0884-5
M3 - Article
AN - SCOPUS:84867399267
SN - 0254-5330
VL - 200
SP - 109
EP - 130
JO - Annals of Operations Research
JF - Annals of Operations Research
IS - 1
ER -