A Class Of Smooth Approximation Methods For Solving Probabilistic Constrained Optimization Problems

Many practical problems with important values,such as calculation of risk value in risk optimization,systemic scheduling problem with new energy and power,route location processing in mobile networks,and so on,belong to probabilistic constrained optimization problem,which requires that random constraints should be satisfied with a large enough probability Simultaneously.Typical solving methods including convex conservative approximation method?D.C.approximation method,?smooth approximation method etc.In view of non-differentiability of probability constrained functions,this thesis studies a class of smooth approximation methods for solving probabilistic constrained optimization problems.The theoretical framework and algorithm design of this class of methods are established.The main results are as follows:Chapter 1 introduces the research status of random optimization problems with probabili-ty constraints.Chapter 2 defines a class of smooth approximation functions(p(z,?)for characteristic function 1(0,+?)(z),and presents the assumptions fulfilled by the functions.Based on this class of functions,smooth approximation functions of probabilistic constrained function p(x)are constructed,and two special cases are given to illustrate.Chapter 3 establishes the smooth approximation problems of problem(P)based on the proposed smooth approximation functions(p?).It is proved that the optimal solution set and optimal value of the problem(p?)converge to the optimal solution set and optimal value of the problem(P)respectively when the parameter ??;The KKT point set of the problem(p?)approximates one of problem(P).Consequently,the solution to the problem(p?)is an approximate solution to the problem(P).In Chapter 4,the smooth DC approximation problem(PDC?)of the problem(p?)is constructed and sequence convex approximation algorithm is proposed to solve the problem.In each iteration of the algorithm,a gradient-based Monte Carlo method is used to solve the convex subproblem(P(?,y)).The limit point of the solution sequences obtained by this algorithm is the KKT point of the problem(PDC?).In Chapter 5,sequence convex approximation algorithm program is written in Matlab language.Sequence convex approximation methods based on Pinar-Zenios smooth sum function and Sigmoid function are used to solve a specific probability constrained optimization problem respectively,and corresponding numerical results are reported.The numerical results illustrate that the proposed smooth approximation methods are effective for solving some probabilistic constrained optimization problems.