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-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.

arXiv admin note: substantial text overlap with arXiv:1406.0724

References in corpus (8)

• Splitting methods with variable metric for KL functions
• An inertial alternating direction method of multipliers
• Inertial Douglas-Rachford splitting for monotone inclusion problems
• Proximal Heterogeneous Block Input-Output Method and application to Blind Ptychographic Diffraction Imaging
• Inertial primal-dual algorithms for structured convex optimization
• A general inertial proximal point method for mixed variational inequality problem
• An inertial forward-backward-forward primal-dual splitting algorithm for solving monotone inclusion problems
• An inertial Tseng's type proximal algorithm for nonsmooth and nonconvex optimization problems