Hybrid Riemannian conjugate gradient methods with global convergence properties

Hiroyuki Sakai () and Hideaki Iiduka ()
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Hiroyuki Sakai: Meiji University
Hideaki Iiduka: Meiji University

Computational Optimization and Applications, 2020, vol. 77, issue 3, No 9, 830 pages

Abstract: Abstract This paper presents Riemannian conjugate gradient methods and global convergence analyses under the strong Wolfe conditions. The main idea of the proposed methods is to combine the good global convergence properties of the Dai–Yuan method with the efficient numerical performance of the Hestenes–Stiefel method. One of the proposed algorithms is a generalization to Riemannian manifolds of the hybrid conjugate gradient method of the Dai and Yuan in Euclidean space. The proposed methods are compared well numerically with the existing methods for solving several Riemannian optimization problems. Python implementations of the methods used in the numerical experiments are available at https://github.com/iiduka-researches/202008-hybrid-rcg .

Keywords: Conjugate gradient method; Riemannian optimization; Hybrid conjugate gradient method; Global convergence; Strong Wolfe conditions (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (4)

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DOI: 10.1007/s10589-020-00224-9

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