WIAS Preprint No. 1089, (2006)

Structural properties of linear probabilistic constraints


  • Henrion, René
    ORCID: 0000-0001-5572-7213

2010 Mathematics Subject Classification

  • 90C15


  • probabilistic constraints, stochastic programming, chance constraints, stochastic optimization




The paper provides a structural analysis of the feasible set defined by linear probabilistic constraints. Emphasis is laid on single (individual) probabilistic constraints. A classical convexity result by Van de Panne/Popp and Kataoka is extended to a broader class of distributions and to more general functions of the decision vector. The range of probability levels for which convexity can be expected is exactly identified. Apart from convexity, also nontriviality and compactness of thefeasible set are precisely characterized at the same time. The relation between feasible sets with negative and nonnegative right-hand side is revealed. Finally, an existence result is formulated for the more difficult case of joint probabilistic constraints.

Appeared in

  • Optimization, 56 (2007) pp. 425--440.

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