Bregman Proximal Gradient Algorithm with Extrapolation for a Class of Nonconvex Nonsmooth Minimization Problems

Zhang X ; Barrio, Roberto (Universidad de Zaragoza) ; Martínez, M. Ángeles (Universidad de Zaragoza) ; Jiang, Hao ; Cheng, Lizhi

Resumen: 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.

Idioma: Inglés

DOI: 10.1109/ACCESS.2019.2937005

Año: 2019

Publicado en: IEEE Access 7 (2019), 126515-126529
ISSN: 2169-3536

Factor impacto JCR: 3.745 (2019)

Categ. JCR: COMPUTER SCIENCE, INFORMATION SYSTEMS rank: 35 / 155 = 0.226 (2019) - Q1 - T1
Categ. JCR: ENGINEERING, ELECTRICAL & ELECTRONIC rank: 61 / 265 = 0.23 (2019) - Q1 - T1
Categ. JCR: TELECOMMUNICATIONS rank: 26 / 89 = 0.292 (2019) - Q2 - T1

Factor impacto SCIMAGO: 0.775 - Engineering (miscellaneous) (Q1) - Computer Science (miscellaneous) (Q1) - Materials Science (miscellaneous) (Q2)

Financiación: info:eu-repo/grantAgreement/ES/DGA-FEDER/E24-17R
Financiación: info:eu-repo/grantAgreement/ES/MICINN/PGC2018-096026-B-I00
Financiación: info:eu-repo/grantAgreement/ES/MICINN/MTM2015-64095-P

Tipo y forma: Article (Published version)

Área (Departamento): Área Matemática Aplicada (Dpto. Matemática Aplicada)