Hybrid Riemannian Conjugate Gradient Methods with Global Convergence Properties

2020/02/05 by Hiroyuki Sakai, Sakai, Hiroyuki, Hideaki Iiduka +1 · 1 citation
Computer Science · Mathematics · #57R35 #65K05 #90C26 #Advanced Optimization Algorithms Research #FOS: Mathematics #Iterative Methods for Nonlinear Equations #Matrix Theory and Algorithms #Optimization and Control (math.OC)

paper · pdf · doi:10.48550/arxiv.2002.01644

openalex publication_date 2020/02/05 · openalex created_date 2020/02/14 · openalex updated_date 2026/07/28

Abstract

This paper presents new Riemannian conjugate gradient methods and global convergence analyses under the strong Wolfe conditions. The main idea of the new methods is to combine the good global convergence properties of the Dai-Yuan method with the efficient numerical performance of the Hestenes-Stiefel method. The proposed methods compare well numerically with the existing methods for the Rayleigh quotient minimization problem on the unit sphere. Numerical comparisons show that they perform better than the existing ones.

Citations

• Function minimization by conjugate gradients
• Benchmarking optimization software with performance profiles

Cited by

• A Riemannian conjugate subgradient method for nonconvex and nonsmooth optimization on manifolds

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