A primal-dual interior point trust-region method for nonlinear semidefinite programming. (4th May 2021)

• Record Type: Journal Article
• Authors: Yamashita, Hiroshi; Yabe, Hiroshi; Harada, Kouhei
• Is Part Of: Optimization methods and software. Volume 36:Number 2/3(2021)
• Page Start: 569
• Page End: 601
• Publication Date: 2021-05-04
• Subjects: Nonlinear semidefinite programming -- primal-dual interior point method -- trust-region method -- barrier penalty function -- primal-dual merit function -- global convergence; 90C22 -- 90C26 -- 90C51; Mathematical optimization -- Periodicals; Algorithms -- Periodicals; 519.7
• DOI: 10.1080/10556788.2020.1801678
• Languages: English
• ISSNs: 1055-6788

Abstract

Abstract : In this paper, we propose a primal-dual interior point trust-region method for solving nonlinear semidefinite programming problems. The method consists of the outer iteration (SDPIP) that finds a Karush–Kuhn–Tucker (KKT) point and the inner iteration (SDPTR) that calculates an approximate barrier KKT point. Algorithm SDPTR combines a commutative class of Newton-like directions with the steepest descent type direction within the framework of the trust-region strategy. We present a trust-region method in primal-dual space and prove the global convergence property of the proposed method. Some numerical experiments are given. In addition, we also present second-order approximations to the primal-dual merit function, and a trust-region method in primal space in Appendix.