Bart Paul Gerard van Parys

Distributionally robust expectation inequalities for structured distributions

  • Paul J. Goulart
  • Bart Paul Gerard van Parys
  • Manfred Morari
    • Categories Convex Optimization, Semi-definite Programming, Stochastic Programming Tags , , ,

    Quantifying the risk of unfortunate events occurring, despite limited distributional information, is a basic problem underlying many practical questions. Indeed, quantifying constraint violation probabilities in distributionally robust programming or judging the risk of financial positions can both be seen to involve risk quantification, notwithstanding distributional ambiguity. In this work we discuss worst-case probability and conditional … Read more

    Generalized Gauss Inequalities via Semidefinite Programming

  • Paul J. Goulart
  • Daniel Kuhn
  • Bart Paul Gerard van Parys
    • Categories Convex Optimization, Statistics, Stochastic Programming Tags , ,

    A sharp upper bound on the probability of a random vector falling outside a polytope, based solely on the first and second moments of its distribution, can be computed efficiently using semidefinite programming. However, this Chebyshev-type bound tends to be overly conservative since it is determined by a discrete worst-case distribution. In this paper we … Read more

    Distributionally robust control of constrained stochastic systems

  • Paul J. Goulart
  • Daniel Kuhn
  • Bart Paul Gerard van Parys
  • Manfred Morari
    • Categories Control Applications, Robust Optimization Tags , ,

    We investigate the control of constrained stochastic linear systems when faced with only limited information regarding the disturbance process, i.e. when only the first two moments of the disturbance distribution are known. We consider two types of distributionally robust constraints. The constraints of the first type are required to hold with a given probability for … Read more