Augmented Lagrangian method for probabilistic optimization

Darinka Dentcheva, Gabriela Martinez

Research output: Contribution to journalArticlepeer-review

20 Scopus citations

Abstract

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.

Original languageEnglish
Pages (from-to)109-130
Number of pages22
JournalAnnals of Operations Research
Volume200
Issue number1
DOIs
StatePublished - Nov 2012

Keywords

  • Chance constraints
  • Probabilistic constraints
  • Second-order optimality conditions
  • Stochastic programming
  • p-efficient points

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