Research On Solving Model Of Two-stage Distributionally Robust Optimization Problem

Two-stage distributionally robust optimization is currently research hotspots with programming uncertainty factor.It overcomes the shortcomings of ordinary two-stage stochastic programming which it needs exactly probability distribution,and has advantages of robust optimization that it is easy to solve.In this thesis,the equivalent model of the two-stage distributionally robust optimization problem are studied.It provides feasible methods to solve more complex practical problems.The main contents are as follows:Firstly,the two-stage distributionally robust linear optimization under the corresponding ambiguity set consisted by second-order moment constraints are studied when the support set of random variables is polyhedron set.When the decision variables of distributionally robust optimization obey the linear decision rules and only the rigt-hand sides are random in the second stage,the two-stage distributionally robust optimization can be transformed into second-order cone optimization problem which can be solved,respectively.Secondly,two-stage distributionally robust quadratic optimization under the condition of generalized Slater conditions are studied when the support set of random variables is polyhedron.When the moment constraint is the second moment constraint,it is proved that the problem can be transformed into a solvable cone optimization problem.When the ambiguity set constraints is high-order moment constraints,and the decision variables in the second stage optimization problem is linear decision rules,the equivalent semi-infinite programming problem are established.At the same time,it is proved that when the moment constraints of the ambiguity set consists high-order moment constraints,and the rigt-hand sides in the second stage optimization problem are only random,the corresponding optimization problem is also equivalent to the solvable semi-infinite programming.Finally,the results indicate that the equivalent model is feasible and it is better than the ordinary two-stage stochastic programming problem.Chart: 3,references: 52.