Research Of Semidefinite Programming And Its Application

Semidefinite programming is an extension of linear programming. In recent years ,the theory and algorithm for semidefinite programming have developed greatly,and its most important applications are found in combinatorial optimization, system engineering and electrical engineering. Semidefinite programming is a new and important research field in mathematical programming.In the paper,we firstly summarize the theory, algorithm, application and recent research of semidefinite programming, then, introduce our some work in algorithm and application. For detail,we conclude them as follows:1. The optimal condition is transformed to a variational inequality. A new protective algorithm is proposed in order to obtain the solution of semidefinite programming by solving variational inequality, and the convergent result was given. The experiments show that the performance of our method is effective.2. An equivalent integral programming model and a new semidefinite programming relaxation for the max-bisection problem are given. Then, we solve the relaxation with a nonlinear programming of low-rank. Coupled with the randomized method, an approximate solution of the max-bisection problem is obtained. The numerical results show that the method can effectively solve the max-bisection problem.3. By means of nonsmooth analysis and convexity, eigenvalue optimization problem is researched in theory,it is helpful to solve the problem.