Robust Optimization Of Two Stage Model

In this paper,we mainly focus on a class of robust optimization problems,namely distri-butionally robust optimization problem which maximaizes the expected value of a objective function when the underlying distribution is ambiguous and therefore robustness is relevant.we introduce a kind of soft robust method which processes the uncertainty set in a smooth way by set partitioning.And the soft robust method connects closely to the theory of convex risk mea-sures to get a new equation.Finally,the results are applied to the two stage robust optimization problemThe main content is organized as following:In the second chapter,it introduces some basic knowledge of convex analysis which includes the related properties of conjugate functions and the basic knowledge of probability which in-cludes the absolute continuity of measure.In the third chapter,it introduces the basic theory of soft robust optimization and the related risk measurement function.And we give an example to explain the feasibility.In the fourth chapter,it introduces the theory of stochastic two stage models.In the fifth chapter,it gives the soft robust optimization of the two stage model and it also proves the equivalence of constraint sets.At last,we give the equivalence of the soft robust optimization of the two stage model.