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arXiv · 1410.0641

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

Radu Ioan Bot·Ernö Robert Csetnek·Szilárd László
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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-\L{}ojasiewicz 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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Radu Ioan Bot, Ernö Robert Csetnek, Szilárd László. 2014-10-02. An inertial forward-backward algorithm for the minimization of the sum of two nonconvex functions. https://arxiv.org/abs/1410.0641

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