A superlinearly convergent SSDP algorithm for nonlinear semidefinite programming

Journal of Inequalities and Applications

Hui Zhang¹  Jian Ling Li¹ 

[1] College of Mathematics and Information Science, Guangxi University;

关键词: Nonlinear semidefinite programming;    Penalty function;    Sequential semidefinite programming;    Global convergence;    Superlinear convergence;   

DOI  :  10.1186/s13660-019-2171-y

来源: DOAJ

【 摘 要 】

Abstract In this paper, we present a sequential semidefinite programming (SSDP) algorithm for nonlinear semidefinite programming. 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 Maratos effect, a second-order correction direction is determined by solving a new quadratic programming. And then a penalty function is used as a merit function for arc search. The superlinear convergence is shown under the strict complementarity and the strong second-order sufficient conditions with the sigma term. Finally, some preliminary numerical results are reported.

【 授权许可】

Unknown