A Simulation Based Approach to Solve A Specific Type of Chance Constrained Optimization

Abstract

We solve the chance constrained optimization with convexfeasible set through approximating the chance constraint by another convexsmooth function. The approximation is based on the numerical properties of theBernstein polynomial that is capable of effectively controlling the approximationerror for both function value and gradient. Thus we adopt a first-order algorithmto reach a satisfactory solution which is expected to be optimal. When theexplicit expression of joint distribution is not available, we then use Monte Carloapproach to numerically evaluate the chance constraint to obtain an optimalsolution by probability. Numerical results for known problem instances arepresented.