In this paper, we consider an accelerated method for solving nonconvex and nonsmooth minimization problems. We propose a bregman proximal gradient algorithm with extrapolation (BPGe). This algorithm extends and accele...
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In this paper, we consider an accelerated method for solving nonconvex and nonsmooth minimization problems. We propose a bregman proximal gradient algorithm with extrapolation (BPGe). This algorithm extends and accelerates the bregmanproximalgradientalgorithm (BPG), which circumvents the restrictive global Lipschitz gradient continuity assumption needed in proximalgradientalgorithms (PG). The BPGe algorithm has a greater generality than the recently introduced proximalgradientalgorithm with extrapolation (PGe) and, in addition, due to the extrapolation step, BPGe converges faster than the BPG algorithm. Analyzing the convergence, we prove that any limit point of the sequence generated by BPGe is a stationary point of the problem by choosing the parameters properly. Besides, assuming Kurdyka-Lojasiewicz property, we prove that all the sequences generated by BPGe converge to a stationary point. Finally, to illustrate the potential of the new method BPGe, we apply it to two important practical problems that arise in many fundamental applications (and that not satisfy global Lipschitz gradient continuity assumption): Poisson linear inverse problems and quadratic inverse problems. In the tests the accelerated BPGe algorithm shows faster convergence results, giving an interesting new algorithm.
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