학술논문
Local convergence of primal–dual interior point methods for nonlinear semidefinite optimization using the Monteiro–Tsuchiya family of search directions
Document Type
Original Paper
Author
Source
Computational Optimization and Applications: An International Journal. 88(2):677-718
Subject
Language
English
ISSN
0926-6003
1573-2894
1573-2894
Abstract
The recent advance of algorithms for nonlinear semidefinite optimization problems (NSDPs) is remarkable. Yamashita et al. first proposed a primal–dual interior point method (PDIPM) for solving NSDPs using the family of Monteiro–Zhang (MZ) search directions. Since then, various kinds of PDIPMs have been proposed for NSDPs, but, as far as we know, all of them are based on the MZ family. In this paper, we present a PDIPM equipped with the family of Monteiro–Tsuchiya (MT) directions, which were originally devised for solving linear semidefinite optimization problems as were the MZ family. We further prove local superlinear convergence to a Karush–Kuhn–Tucker point of the NSDP in the presence of certain general assumptions on scaling matrices, which are used in producing the MT search directions. Finally, we conduct numerical experiments to compare the efficiency among members of the MT family.