The Methods For Solving Two Kinds Of Distributionally Robust Optimization Problems

Several methods of solving distributed robust optimization problem based on several divergence measures are introduced in this paper.The model is studied as follows where,(?)The central idea of this paper is to define the uncertainty set ? phased on the divergence,on the premise of the known empirical distribution,using distance empirical distribution is not more than a positive number to define distribution set.Selecting different divergence measures,and the above mentioned optimization model is transformed into a convex and non-convex robust optimization model.According to different models,we choose different ways to solve them.Specifically,a randomized method is proposed and sample is taken by Monte Carlo,and assume sample?1,…,?N is a set of independent identically distributed.First,under the assumption that the set is continuous,the approximate model of the original optimization model is obtained by Lagrange dual as well as discrete support set of random variables.The robust optimization model with convex distribution is proved,its optimal solution of the approximate model converges to the optimal solution of the original problem;and for the robust optimization model with non convex distribution,its stable points of the approximate model converge to the stable points of the original problem.Second,for the robust optimization model with convex distribution,the tangent plane algorithm and convergence theorem are given for continuous uncertain set and discrete uncertain set respectively.Finally,the variational inequality theory is applied to the convex distribution robust optimization problem.The saddle point of the optimization problem is obtained according to the stepwise decomposition algorithm.The main structure of this paper is as follows.In the first chapter,the research background and preliminary knowledge are given.In the second chapter,a method for solving two classes of robust optimization models with convex and non-convex distribution is presented,and for the convex optimization model,the tangent plane method is used to solve the model when the uncertain set is continuous.The third chapter is the tangent plane method to solve the convex distribution robust optimization model in the discrete uncertain set,the variational inequality theory is applied in the fourth to find the saddle point of the optimization problem by the step-by-step decomposition algorithm,and the last chapter gives the scientific experiment results.