Scenario Approximations of Chance Constraints

  title={Scenario Approximations of Chance Constraints},
  author={Arkadi Nemirovski and Alexander Shapiro},
We consider an optimization problem of minimization of a linear function subject to the chance constraint Prob{G(x, ξ) ∈ C} ≥ 1 − ε, where C is a convex set, G(x, ξ) is bi-affine mapping and ξ is a vector of random perturbations with known distribution. When C is multi-dimensional and ε is small, like 10−6 or 10−10, this problem is, generically, a problem of minimizing under a nonconvex and difficult to compute constraint and as such is computationally intractable. We investigate the potential… CONTINUE READING
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