WIAS Preprint No. 2569, (2019)

Generalized gradients for probabilistic/robust (probust) constraints


  • van Ackooij, Wim
  • Henrion, René
    ORCID: 0000-0001-5572-7213
  • Pérez-Aros, Pedro

2010 Mathematics Subject Classification

  • 90C15


  • Stochastic optimization, probabilistic constraints, chance constraints, gradients of probability functions, probust constraints




Probability functions are a powerful modelling tool when seeking to account for uncertainty in optimization problems. In practice, such uncertainty may result from different sources for which unequal information is available. A convenient combination with ideas from robust optimization then leads to probust functions, i.e., probability functions acting on generalized semi-infinite inequality systems. In this paper we employ the powerful variational tools developed by Boris Mordukhovich to study generalized differentiation of such probust functions. We also provide explicit outer estimates of the generalized subdifferentials in terms of nominal data.

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