Ambiguous Probabilistic Constrained Optimization Problem Based On Burg Entropy-divergence Function

Many practical problems with important values can be modeled as probabilistic optimization problems,such as reservoir system design,cash matching,and so on,which often exist uncertainty distribution.Therefore,the key to solving this kind of problem is to specify ambiguity set for distribution.This paper focus on uncertainty of probability distribution based on Burg entropy-divergence function.An equivalent form of ambiguous probabilistic constraint is obtained.The ambiguous probabilistic constrained optimization problem is transformed into a probabilistic constrained optimization problem with unique confidence level.The equivalent D.C.approximation problem is built and solved by sequential convex approximation method.Main results are summarized as follows.Chapter 1 reviews research background of ambiguous probability optimization problem and introduces some preliminary knowledge.Chapter 2 discusses an equivalent form of uncertain probability constraint based on Burg entropy-divergence function.Firstly,Burg entropy-divergence is defined based on Burg entropy-divergence function.Furthermore,ambiguity set for distribution is specified.Secondly,With the change-of-measure technique,the optimization problem with respect to distribution P is converted to a convex optimization with respect to likelihood ratio.Existence of solutions of the convex optimization is proved.Consequently,we obtain the equivalent form of ambiguous probabilistic constraint.Chapter 3 establishes an equivalent forms of ambiguous probability constrained optimization problem.Firstly,it proves that uncertain probability optimization problem can be transformed into certain probability constrained optimization problem with unique confidence level.A new confidence level is calculated by bisection method.Secondly,both CVaR approximation and D.C.approximation are constructed.Finally it introduces sequential convex approximation method to solve D.C approximation problem.