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An inertial forward-backward algorithm for the minimization of the sum of two nonconvex functions

Radu Ioan Bot(radu.bot***at***univie.ac.at)
Ernö Robert Csetnek(ernoe.robert.csetnek***at***univie.ac.at)
Szilard Laszlo(szilard.laszlo***at***math.utcluj.ro)

Abstract: We propose a forward-backward proximal-type algorithm with inertial/memory effects for minimizing the sum of a nonsmooth function with a smooth one in the nonconvex setting. The sequence of iterates generated by the algorithm converges to a critical point of the objective function provided an appropriate regularization of the objective satisfies the Kurdyka-Lojasiewicz inequality, which is for instance fulfilled for semi-algebraic functions. We illustrate the theoretical results by considering two numerical experiments: the first one concerns the ability of recovering the local optimal solutions of nonconvex optimization problems, while the second one refers to the restoration of a noisy blurred image.

Keywords: nonsmooth optimization, limiting subdifferential, Kurdyka-Lojasiewicz inequality, Bregman distance, inertial proximal algorithm

Category 1: Convex and Nonsmooth Optimization (Nonsmooth Optimization )

Citation:

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Entry Submitted: 10/02/2014
Entry Accepted: 10/02/2014
Entry Last Modified: 10/02/2014

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