Research On Some Problems Of Quadratic Semidefinite Programmings

Some problems on the quadratic semidefinite programming are discussed, and algorithms for the quadratic semidefinite programming are designed in this article. This paper mainly consists of three sections.In the first section, we introduce a series of studies of the past two decades scholars semidefinite programming done.In the second section, the primal dual interior algorithm for the linear semidef-inite programming is generalized to solve a class of quadratic semidefinite program-ming. The K..S..H direction of the algorithm is obtained via solving a system of nonlinear equations by the classic Newton method, and the existence and uniqueness of the direction is proved. Finally, a specific framework of the primal dual interior algorithm for the quadratic semidefinite programming is presented based on K.. S.. H search direction, whose feasibility is verified through the examples calculated in MATLAB.In the third section, firstly we give a brief introduction to the relation between semidefinite least squares problem and quadratic semidefinite programming,secondly we mainly extend the direction of Gauss-Newton in semidefinite programming to a special class of quadratic semidefinite programming, then change the primal problem to the linear least semedifinite square problem under the guide of the theory of matrix and NT-direction of primal-dual algorithm. We finally prove the existence and uniqueness of the Gauss-Newton search direction.