Cheng: Computationally Efficient Reformulations and Approximations for Chance Constrained Optimization

Chance constrained Optimization (CCO) is one of the main topics in stochastic programming for dealing with random parameters in optimization problems.  Since firstly introduced by Charnes, Cooper and Symonds in 1958, CCO has attracted significant attention of many researchers and practitioners as it plays an important role in engineering, telecommunication, finance, etc.  However, limited progress was made until recently, due to its computational difficulty for two main reasons.

First, feasible sets of CCO problems are generally not convex except in a few special cases. Therefore, it is difficult to  find a globally optimal solution. Second, even for a convex optimization problem, it is difficult to check the feasibility of a candidate solution as this generally requires multi-dimensional integration. Consequently, a large body of research have focused on developing approximation methods to find high-quality solutions within practical time limitations. In this talk, we first briefly introduce CCO, including the basic idea and a brief survey of the state-of-art. Then we present several computationally efficient reformulations and approximations for certain CCP problems. At the end, we conclude with some future research directions that may be of interest to Math586 students.