A primal-dual interior point method for nonlinear semidefinite programming

• 成果类型: Article
• 署名作者: Yamashita, Hiroshi; Yabe, Hiroshi; Harada, Kouhei
• 署名单位: Tokyo University of Science
• 刊物名称: MATHEMATICAL PROGRAMMING
• ISSN/ISSBN: 0025-5610
• DOI: 10.1007/s10107-011-0449-z
• 发表日期: 2012
• 页码: 89-121
• 关键词: robust-control; CONVERGENCE

摘要

This paper is concerned with a primal-dual interior point method for solving nonlinear semidefinite programming problems. The method consists of the outer iteration (SDPIP) that finds a KKT point and the inner iteration (SDPLS) that calculates an approximate barrier KKT point. Algorithm SDPLS uses a commutative class of Newton-like directions for the generation of line search directions. By combining the primal barrier penalty function and the primal-dual barrier function, a new primal-dual merit function is proposed. We prove the global convergence property of our method. Finally some numerical experiments are given.