A D.C. approximation approach for optimization with probabilistic constraints based on Chen–Harker–Kanzow–Smale smooth plus function

Abstract

Many important practical problems can be formulated as probabilistic constrained optimization problem (PCOP), which is challenging to solve since it is usually non-convex and non-smooth. Effective methods for (PCOP) mostly focus on approximation techniques. This paper aims at studying the D.C. (difference of two convex functions) approximation techniques. A D.C. approximation is explored to solve the probabilistic constrained optimization problem based on Chen–Harker–Kanzow–Smale (CHKS) smooth plus function. A smooth approximation to probabilistic constraint function is proposed and the corresponding D.C. approximation problem is established. It is proved that the approximation problem is equivalent to the original one under certain conditions. Sequential convex approximation (SCA) algorithm is implemented to solve the D.C. approximation problem. Sample average approximation method is applied to solve the convex subproblem. Numerical results suggest that D.C. approximation technique is effective for optimization with probabilistic constraints.