An inertial forward-backward algorithm for the minimization of the sum of two nonconvex functions
This work provides a theoretical convergence guarantee for an inertial proximal algorithm in nonconvex optimization, which is relevant for researchers in optimization and signal processing.
The paper proposes an inertial forward-backward algorithm for minimizing sums of nonconvex functions and proves convergence to critical points under the Kurdyka-Łojasiewicz inequality. Numerical experiments show recovery of local optima and image restoration.
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.