Chance constrained optimization problem is a very important topic in the stochastic optimization literature. In this paper, we first give an overview on chance constrained programming and its current solving methods. We next discuss in detail the popular convex approximation for chance constrained programming - conditional value at risk (CVaR) approximation which has very nice properties due to its convexity, computational efficiency and its nearing to the original probabilistic constraints....[ Read more ]

Chance constrained optimization problem is a very important topic in the stochastic optimization literature. In this paper, we first give an overview on chance constrained programming and its current solving methods. We next discuss in detail the popular convex approximation for chance constrained programming - conditional value at risk (CVaR) approximation which has very nice properties due to its convexity, computational efficiency and its nearing to the original probabilistic constraints.

Based on the CVaR approximation, we propose an equivalent difference of convex (DC) formulation of the chance constraints. Such DC optimization problem can be solved by a sequence of convex approximations. We find that starting from the optimal solution of CVaR approximation, we can further improve it iteratively to a local optimal of chance constrained problem. This provides a way for trading off the time complexity and the quality of solutions.

Finally, we show the comparison between one step convex (CVaR i.e.) approximation and sequential convex approximations by three important real world applications.