An inertial forward-backward algorithm for the minimization of the sum of two nonconvex functions
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.
Keywords
Cite
@article{arxiv.1410.0641,
title = {An inertial forward-backward algorithm for the minimization of the sum of two nonconvex functions},
author = {Radu Ioan Bot and Ernö Robert Csetnek and Szilárd László},
journal= {arXiv preprint arXiv:1410.0641},
year = {2014}
}
Comments
arXiv admin note: substantial text overlap with arXiv:1406.0724