Two SSDP Algorithms For Nonlinear Semidefinite Programming

In this thesis,nonlinear semidefinite programming(NLSDP)problems are investigated.NLSDP has many applications such as engineering,econo-my,optimal structural design,truss design problems,etc.Therefore,research-ing on stable and efficient numerical algorithms for NLSDP has important theoretical significance and applied value.First of all,in this thesis,a sequential semidefinite programming al-gorithm for nonlinear semidefinite programming with matrix inequality,is proposed.At each iteration,a linear semidefinite programming subproblem and a modified quadratic semidefinite programming subproblem are solved to generate a master search direction.In order to avoid the Maratos effect,a second-order correction direction is generated by solving system of linear equations;And then a penalty function is used as a merit function for curve search which ensures that the merit function is sufficiently reduced.The su-perlinear convergence is shown under some mild conditions.The numerical results indicate that the proposed algorithm is effective and comparable.Secondly,in this thesis,a sequential semidefinite programming algorith-m for nonlinear semidefinite programming with general constraints.At each iteration,search direction is yielded by a specially structured semidefinite programming subproblem and a modified quadratic semidefinite program-ming subproblem.And a distance function is introduced and it is used to construct a merit function for curve search.The curve search ensures that the merit function is sufficiently reduced;The penalty parameter is updated automatically in the iterative process.Under some appropriate assumptions,the global convergence are shown.Some numerical results are reported.