Primal-dual predictor-corrector interior point algorithm for quadratic semidefinite programming

This paper extends the interior point algorithm for solving Semidefinite Programming(SDP) to Quadratic Semidefinite Programming(QSDP) and especially discusses the generation of AHO search direction.Firstly,we derive the nonlinear equations for solving QSDP using Wolfe's dual theorem.The AHO search direction is got by applying Newton's method to the equations.Then we prove the existence and uniqueness of the search direction,and give the detaied steps of predictor-corrector interior-point algorithm.At last,this paper provides a numerical comparison of the algoritms using three different search directions and suggests the algorithm using NT direction is the most robust.