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

Laszlo Szilard Csaba (laszlosziszi***at***yahoo.com)

Abstract: We investigate an inertial algorithm of gradient type in connection with the minimization of a nonconvex differentiable function. The algorithm is formulated in the spirit of Nesterov's accelerated convex gradient method. We show that the generated sequences converge to a critical point of the objective function, if a regularization of the objective function satis es the Kurdyka-Lojasiewicz property. Further, we provide convergence rates for the generated sequences and the function values formulated in terms of the Lojasiewicz exponent.

Keywords: inertial algorithm, nonconvex optimization, Kurdyka- Lojasiewicz inequality, convergence rate

Category 1: Other Topics (Other )

Citation: S. László, 2018, Technical University of Cluj-Napoca, Department of Mathematics, Str. Memorandumului nr. 28, 400114 Cluj-Napoca, Romania, e-mail: laszlosziszi@yahoo.com

Download: [PDF]

Entry Submitted: 06/19/2018
Entry Accepted: 06/19/2018
Entry Last Modified: 11/22/2018

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