The Research On Duality Theory Of Robust Semi-infinite Optimization Problems

Semi-infinite programming is an optimization problem with infinite number of decision variables or infinite constraint conditions.However,in real life,the mathematical model with the uncertainty of decision variables due to the lack of data,fluctuation and other problems are often used,that is the robust semi-infinite optimization problem.Due to the uncertainty of variables and the infinite constraint conditions,it's very difficult to solve this kind of problem directly.Therefore,in order to better study this kind of problem,the duality of robust semi-infinite programming is discussed and analyzed in this paper.The main research contents of this paper include three aspects.Firstly,the linear semiinfinite problem is discussed by using Fourier-Motzkin elimination method.A new closed convex cone is established,and proved that it is a necessary and sufficient condition for the duality theory.Further the example is given to illustrate that the method of Fourier-Motzkin elimination simplifies the calculation,the closed convex cone established is reasonable,and the duality theorem is valid.Secondly,according to the definition of approximate solutions,the sufficient and necessary conditions for the validity of approximate duality theory for uncertain semi-infinite convex programming problems are given,and the Lagrange duality problem is established.A numerical comparison is made between the original problem and the dual problem.Finally,the multi-objective approximate solution is defined,and the sufficient and necessary conditions for the establishment of the approximate duality theory of uncertain multiobjective semi-infinite problems are established.Set up the Lagrange duality problem.In addition,it's applied to Markowitz Mean-Variance model in economic market activities,from which a multi-objective linear semi-infinite programming model with uncertain parameters is extracted.And the dual problem is presented.