Study On Discretization Method And Duality Theory For Semidefinite Programming

Semidefinite programming is also known as linear programming with positive semidefinite cone constraints,and linear programming is one kind of it.This paper will consider a discretization method of semidefinite programming and optimality conditions and duality theory of multiobjective semidefinite programming.To specific:1.A new approximate algorithm for solving semidefinite programs and a new method for proving the strong duality theorem of the semidefinite programming problems are proposed.Firstly,we reprove the semidefinite programs' Lagrangian strong duality theorem by use of the linear programming problems'strong duality theorem and discretization idea.Secondly,we propose a new approximate algorithm for solving semidefinite programs via a discreatization method.At last,we provide some numerical experiment results.2.First of all,we define a class of generalized I type function for multiobjective semidefinite programmings.Secondly,optimality sufficient conditions are given under the definition of generalized I type function of multiobjective semidefinite program-mings.Finally,Wolfe dual and Mond-Weir dual model for multiobjective seinidefinite programming problems are considered.We give and prove the duality theorems.