When there is parameter uncertainty in the constraints of a convex optimization problem, it is natural to formulate the problem as a joint chance constrained program (JCCP), which requires that all constraints be satisfied simultaneously with a given large probability. In this paper, we propose to solve the JCCP by a sequence of convex approximations. We show that the solutions of the sequence of approximations converge to a Karush-Kuhn-Tucker (KKT) point of the JCCP under a certain asymptotic regime. Furthermore, we propose to use a gradient-based Monte Carlo method to solve the sequence of convex approximations.
Hong et al. REF propose a sequence of conservative nonsmooth difference-of-convex (DC) approximations of the step function and use it to solve joint chance-constrained convex programs.
Sequential Convex Approximations to Joint Chance Constrained Programs: A Monte Carlo Approach
Oper. Res.
Oper. Res.
Computer Science Mathematics