Convergence rates for an inertial algorithm of gradient type associated\n to a smooth nonconvex minimization

2018/07/01 by Szilárd Csaba László, László, Szilárd Csaba · 2 citations
Computer Science · Mathematics · #65K10 #90C26 #90C30 #FOS: Mathematics #Functional Analysis (math.FA) #Numerical methods in inverse problems #Optimization and Variational Analysis

paper · pdf · doi:10.48550/arxiv.1807.00387

openalex publication_date 2018/07/01 · openalex created_date 2022/11/15 · openalex updated_date 2026/07/28

Abstract

We investigate an inertial algorithm of gradient type in connection with the\nminimization of a nonconvex differentiable function. The algorithm is\nformulated in the spirit of Nesterov's accelerated convex gradient method. We\nshow that the generated sequences converge to a critical point of the objective\nfunction, if a regularization of the objective function satisfies the\nKurdyka- Lojasiewicz property. Further, we provide convergence rates for the\ngenerated sequences and the function values formulated in terms of the\n Lojasiewicz exponent.\n

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