Discontinuous penalty approach with deviation integral for global constrained minimization

In this paper, we use the discontinuous exact penalty functions to solve the constrained minimization problems with an integral approach. We examine a general form of the constrained deviation integral and its analytical properties. The optimality conditions of the penalized minimization problems are proven. To implement the algorithm, the cross-entropy method and the importance sampling are used based on the Monte-Carlo technique. Numerical tests show the effectiveness of the proposed algorithm.