This paper discusses joint rectangular geometric chance constrained programs. When the stochastic parameters are elliptically distributed and pairwise independent, we present a reformulation of the joint rectangular geometric chance constrained programs. As the reformulation is not convex, we propose new convex approximations based on variable transformation together with piecewise linear appro...

We propose a stochastic algorithm for the global optimization of chance constrained problems. We assume that the probability measure with which the constraints are evaluated is known only through its moments. The algorithm proceeds in two phases. In the first phase the probability distribution is (coarsely) discretized and solved to global optimality using a stochastic algorithm. We only assume...

Chance constrained programming is an effective and convenient approach to control riskin decision making under uncertainty. However, due to unknown probability distributions ofrandom parameters, the solution obtained from a chance constrained optimization problem canbe biased. In addition, instead of knowing the true distributions of random parameters, inpractice, only a series ...

We consider chance-constrained programs in which the probability distribution of the random parameters is deterministic and known. Two prominent approaches to deal with these programs are sampling approximations and robust approximations. In the last decade, there has been enormous interest in both these areas of research. This article aims to provide a brief summary of a select number of publi...

In this paper we study ambiguous chance constrained problems where the distributions of the random parameters in the problem are themselves uncertain. We focus primarily on the special case where the uncertainty set Q of the distributions is of the form Q = {Q : ρp(Q, Q0) ≤ β}, where ρp denotes the Prohorov metric. The ambiguous chance constrained problem is approximated by a robust sampled pro...