A Primal-dual Interior-point Method For Nonlinear Semidefinite Programming

In this thesis,nonlinear semidefinite programming is investigated with equality constraints and a positive semidefinite matrix constraint.This kind of problems is widely used in control theory,eigenvalue optimization,finance,etc.So it is necessary to study its solution algorithm.In this thesis,a primal dual interior point method is proposed to solve nonlinear semidefinite programming.Firstly,the KKT conditions of nonlinear semidefinite programming are perturbed.Then,based on the perturbed KKT conditions,we derive a set of linear equations by Newton method to generate search directions.The algorithm of this thesis consists of an outer iteration and an inner iteration.The outer iteration is implemented by algorithm A to generate the KKT point of nonlinear semidefinite programming;The inner iteration is implemented by Algorithm B to generate an approximate perturbed KKT point.In the inner iteration,a new merit function is introduced to generate steps by line search.Under some appropriate assumptions,the proposed algorithm possesses global convergence.Finally,a preliminary numerical test is carried out on the proposed algorithm.Especially,the numerical results of the two scaling matrices are compared.The numerical results show that the proposed algorithm is feasible and effective.