The Proximal Gradient Method for Composite Optimization Problems on Riemannian Manifolds

Xiaobo Li ()
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Xiaobo Li: School of Sciences, Civil Aviation Flight University of China, Guanghan 618300, China

Mathematics, 2024, vol. 12, issue 17, 1-15

Abstract: In this paper, the composite optimization problem is studied on Riemannian manifolds. To tackle this problem, the proximal gradient method to solve composite optimization problems is proposed on Riemannian manifolds. Under some reasonable conditions, the convergence of the proximal gradient method with the backtracking procedure in the nonconvex case is presented. Furthermore, a sublinear convergence rate and the complexity result of the proximal gradient method for convex case are also established on Riemannian manifolds.

Keywords: composite optimization problems; the proximal gradient method; convergence result; Riemannian manifolds (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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