2011/03/24 by G. C. Bento, Bento, G. C., João Xavier da Cruz Neto +3 · 1 citation
Computer Science · Mathematics · #40A05 #47J25 #49J52 #49M37 #58C99 #65K05 #65K15 #90C26 #90C56 #Advanced Optimization Algorithms Research #FOS: Mathematics #Numerical Analysis (math.NA) #Numerical methods in inverse problems #Optimization and Variational Analysis
paper · pdf · doi:10.48550/arxiv.1103.4828
openalex publication_date 2011/03/24 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
In this paper we present an abstract convergence analysis of inexact descent methods in Riemannian context for functions satisfying Kurdyka-Lojasiewicz inequality. In particular, without any restrictive assumption about the sign of the sectional curvature of the manifold, we obtain full convergence of a bounded sequence generated by the proximal point method, in the case that the objective function is nonsmooth and nonconvex, and the subproblems are determined by a quasi distance which does not necessarily coincide with the Riemannian distance. Moreover, if the objective function is C1 with L-Lipschitz gradient, not necessarily convex, but satisfying Kurdyka-Lojasiewicz inequality, full convergence of a bounded sequence generated by the steepest descent method is obtained.