On tractable approximations of randomly perturbed convex constraints
Arkadi S. Nemirovski · 2004
We consider a chance constraint Prob{/spl xi/ : A(x, /spl xi/) /spl isin/ K} /spl ges/ 1 - e (x is the decision vector, /spl xi/ is a random perturbation, K is a closed convex cone, and A(/spl middot/,/spl middot/) is bilinear). While important for many applications in optimization and control, chance constraints typically are "computationally intractable", which makes it necessary to look for their tractable approximations. We present these approximations for the cases when the underlying conic constraint A(x,/spl xi/)/spl isin/ K is (a) scalar inequality, or (b) conic quadratic inequality, or (c) linear matrix inequality, and discuss the level of conservativeness of the approximations.