A limited-memory Riemannian symmetric rank-one trust-region method with an efficient algorithm for its subproblem⁎The author WH was partially supported by the Fundamental Research Funds for the Central Universities (NO. 20720190060) and National Natural Science Foundation of China (NO. 12001455). The work of KAG is partially supported by the U.S. National Science Foundation under grant DBI 1934157. Issue 9 (2021)

• Record Type: Journal Article
• Authors: Huang, Wen; Gallivan, Kyle A.
• Is Part Of: IFAC-PapersOnLine. Volume 54:Issue 9(2021)
• Page Start: 572
• Page End: 577
• Publication Date: 2021
• Subjects: Riemannian optimization -- limited-memory quasi-Newton -- trust-region -- symmetric rank-one; Automatic control -- Periodicals; 629.805
• DOI: 10.1016/j.ifacol.2021.06.118
• Languages: English
• ISSNs: 2405-8963

Abstract

Abstract: Limited-memory versions of quasi-Newton methods are efficient methods for large-scale optimization problems in the Euclidean space. In particular, a quasi-Newton symmetric rank-one update used in a trust-region setting has proven to be an effective method. In this paper, we present a Riemannian version of a limited-memory symmetric rank-one trust-region method with an efficient algorithm for solving its subproblem. Following a known standard result, we show the global convergence of the proposed method. The numerical experiments are performed to compare our method with other Riemannian optimization methods.