2022/07/05 by Hiroyuki Sakai, Sakai, Hiroyuki, Hiroyuki Satō +3
Computer Science · Mathematics · #57R35 #65K05 #90C26 #Advanced Optimization Algorithms Research #FOS: Mathematics #Matrix Theory and Algorithms #Optimization and Control (math.OC)
paper · pdf · doi:10.48550/arxiv.2207.01855
openalex publication_date 2022/07/05 · openalex created_date 2023/01/01 · openalex updated_date 2026/07/28
This paper presents the Hager-Zhang (HZ)-type Riemannian conjugate gradient method that uses the exponential retraction. We also present global convergence analyses of our proposed method under two kinds of assumptions. Moreover, we numerically compare our proposed methods with the existing methods by solving two kinds of Riemannian optimization problems on the unit sphere. The numerical results show that our proposed method has much better performance than the existing methods, i.e., the FR, DY, PRP and HS methods. In particular, they show that it has much higher performance than existing methods including the hybrid ones in computing the stability number of graphs problem.