A Primal-dual Predictor-corrector Algorithm For Convex Quadratic Semidefinite Programming

In this thesis,a special kind of nonlinear semidefinite programming,i.e.,convex quadratic semidefinite programming(CQSDP for short)is investi-gated.CQSDP has a wide range of applications in the fields of economy,finance,engineering design,control theory and so on.Therefore,the study on algorithms for solving the CQSDP has important practical significance in theory and application.In this thesis,a primal-dual predictor-corrector algorithm for convex quadratic semidefinite programming is presented.Motivated from the idea of primal-dual predictor-corrector method for linear semidefinite program-ming,based on primal dual NT-scaling direction and affine-scaling direction,we propose a primal-dual predictor-corrector algorithm.A central path func-tion is introduced.At each iteration,primal dual NT-scaling direction and affine-scaling direction are used as the search direction for corrector step and predictor step,respectively.The feasibility of the predictor-corrector step and the properties of the central path function at the new iterative point are shown.Under some mild conditions,the proposed algorithm can find an ?-optimal solution in at most O(6nlo2Tr(X0S0)/?)iteretions.Finally,some preliminary numerical results for the proposed algorithms are reported.The numerical results indicate that the proposed algorithm are feasible and effective.