Global Convergence of Hager-Zhang type Riemannian Conjugate Gradient Method
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Publication:6403999
DOI10.1016/J.AMC.2022.127685arXiv2207.01855MaRDI QIDQ6403999
Hiroyuki Sakai, Hiroyuki Sato, Hideaki Iiduka
Publication date: 5 July 2022
Abstract: 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.
Numerical mathematical programming methods (65K05) Nonconvex programming, global optimization (90C26) Methods of quasi-Newton type (90C53) Complementarity and equilibrium problems and variational inequalities (finite dimensions) (aspects of mathematical programming) (90C33) Programming in abstract spaces (90C48)
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