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

2014/10/02 by Bot, Radu Ioan, Csetnek, Ernö Robert, László, Szilárd · 2 citations
#65K10 #90C26 #90C30 #FOS: Mathematics #Numerical Analysis (math.NA) #Optimization and Control (math.OC)

paper · doi:10.48550/arxiv.1410.0641

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-Łojasiewicz 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.

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