On the convergence of a linesearch based proximal-gradient method for nonconvex optimization
Provides theoretical convergence guarantees for a practical algorithm in nonconvex nonsmooth optimization, which is relevant for researchers in optimization and image processing.
The paper proves convergence of a variable metric linesearch proximal gradient method for nonconvex optimization under the Kurdyka-Lojasiewicz property, and demonstrates its flexibility and competitiveness on image processing problems.
We consider a variable metric linesearch based proximal gradient method for the minimization of the sum of a smooth, possibly nonconvex function plus a convex, possibly nonsmooth term. We prove convergence of this iterative algorithm to a critical point if the objective function satisfies the Kurdyka-Lojasiewicz property at each point of its domain, under the assumption that a limit point exists. The proposed method is applied to a wide collection of image processing problems and our numerical tests show that our algorithm results to be flexible, robust and competitive when compared to recently proposed approaches able to address the optimization problems arising in the considered applications.