1. An inertial forward–backward algorithm for the minimization of the sum of two nonconvex functions
- Author
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Radu Ioan Boţ, Ernö Robert Csetnek, and Szilárd Csaba László
- Subjects
90C26 ,90C30 ,65K10 ,Applied mathematics. Quantitative methods ,T57-57.97 ,Electronic computers. Computer science ,QA75.5-76.95 - 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. Every 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.
- Published
- 2016
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