Regularization methods for optimization problems with probabilistic constraints

Darinka Dentcheva, Gabriela Martinez

Research output: Contribution to journalArticlepeer-review

Abstract

We analyze nonlinear stochastic optimization problems with probabilistic constraints on nonlinear inequalities with random right hand sides. We develop two numerical methods with regularization for their numerical solution. The methods are based on first order optimality conditions and successive inner approximations of the feasible set by progressive generation of p-efficient points. The algorithms yield an optimal solution for problems involving α-concave probability distributions. For arbitrary distributions, the algorithms solve the convex hull problem and provide upper and lower bounds for the optimal value and nearly optimal solutions. The methods are compared numerically to two cutting plane methods.

Original languageEnglish
Pages (from-to)223-251
Number of pages29
JournalMathematical Programming
Volume138
Issue number1-2
DOIs
StatePublished - Apr 2013

ASJC Scopus subject areas

  • Software
  • General Mathematics

Keywords

  • Augmented Lagrangian
  • Bundle methods
  • Chance constraints
  • Duality
  • Stochastic programming

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