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In this paper, we present a new scheme of a sampling-based method to solve chance constrained programs. The main advantage of our approach is that the approximation problem contains only continuous variables whilst the standard sample average approximation (SAA) formulation contains binary variables. Although our approach generates new chance constraints, we show that such constraints are tractable under certain conditions. Moreover, we prove that the proposed approach has the same convergence properties as the SAA approach. Finally, numerical experiments show that the proposed approach outperforms the SAA approach on a set of tested instances. [ABSTRACT FROM AUTHOR]

In this paper we develop convex relaxations of chance constrained optimization problems in order to obtain lower bounds on the optimal value. Unlike existing statistical lower bounding techniques, our approach is designed to provide deterministic lower bounds. We show that a version of the proposed scheme leads to a tractable convex relaxation when the chance constraint function is affine with respect to the underlying random vector and the random vector has independent components. We also propose an iterative improvement scheme for refining the bounds. [ABSTRACT FROM AUTHOR]

We consider an n-player finite strategic game. The payoff vector of each player is a random vector whose distribution is not completely known. We assume that the distribution of a random payoff vector of each player belongs to a distributional uncertainty set. We define a distributionally robust chance-constrained game using worst-case chance constraint. We consider two types of distributional uncertainty sets. We show the existence of a mixed strategy Nash equilibrium of a distributionally robust chance-constrained game corresponding to both types of distributional uncertainty sets. For each case, we show a one-to-one correspondence between a Nash equilibrium of a game and a global maximum of a certain mathematical program. [ABSTRACT FROM AUTHOR]