4 research outputs found
Bregman Proximal Gradient Algorithm with Extrapolation for a class of Nonconvex Nonsmooth Minimization Problems
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
Bregman Proximal Gradient algorithm (BPG), which circumvents the restrictive
global Lipschitz gradient continuity assumption needed in Proximal Gradient
algorithms (PG). The BPGe algorithm has higher generality than the recently
introduced Proximal Gradient algorithm with extrapolation(PGe), and besides,
due to the extrapolation step, BPGe converges faster than 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 parameters
properly. Besides, assuming Kurdyka-{\'L}ojasiewicz property, we prove the
whole sequences generated by BPGe converges 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.Comment: Preprint submitted for publication, February 14, 201
Bregman Proximal Gradient Algorithm with Extrapolation for a Class of Nonconvex Nonsmooth Minimization Problems
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 Bregman Proximal Gradient algorithm (BPG), which circumvents the restrictive global Lipschitz gradient continuity assumption needed in Proximal Gradient algorithms (PG). The BPGe algorithm has a greater generality than the recently introduced Proximal Gradient algorithm 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