000084729 001__ 84729
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000084729 0247_ $$2doi$$a10.1109/ACCESS.2019.2937005
000084729 0248_ $$2sideral$$a114050
000084729 037__ $$aART-2019-114050
000084729 041__ $$aeng
000084729 100__ $$aZhang X
000084729 245__ $$aBregman Proximal Gradient Algorithm with Extrapolation for a Class of Nonconvex Nonsmooth Minimization Problems
000084729 260__ $$c2019
000084729 5060_ $$aAccess copy available to the general public$$fUnrestricted
000084729 5203_ $$aIn 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.
000084729 536__ $$9info:eu-repo/grantAgreement/ES/DGA-FEDER/E24-17R$$9info:eu-repo/grantAgreement/ES/MICINN/PGC2018-096026-B-I00$$9info:eu-repo/grantAgreement/ES/MICINN/MTM2015-64095-P
000084729 540__ $$9info:eu-repo/semantics/openAccess$$aAll rights reserved$$uhttp://www.europeana.eu/rights/rr-f/
000084729 590__ $$a3.745$$b2019
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000084729 593__ $$aEngineering (miscellaneous)$$c2019$$dQ1
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000084729 593__ $$aMaterials Science (miscellaneous)$$c2019$$dQ2
000084729 655_4 $$ainfo:eu-repo/semantics/article$$vinfo:eu-repo/semantics/publishedVersion
000084729 700__ $$0(orcid)0000-0002-8089-343X$$aBarrio, Roberto$$uUniversidad de Zaragoza
000084729 700__ $$0(orcid)0000-0002-7374-3222$$aMartínez, M. Ángeles$$uUniversidad de Zaragoza
000084729 700__ $$aJiang, Hao
000084729 700__ $$aCheng, Lizhi
000084729 7102_ $$12005$$2595$$aUniversidad de Zaragoza$$bDpto. Matemática Aplicada$$cÁrea Matemática Aplicada
000084729 773__ $$g7 (2019), 126515-126529$$pIEEE Access$$tIEEE Access$$x2169-3536
000084729 8564_ $$s4872798$$uhttps://zaguan.unizar.es/record/84729/files/texto_completo.pdf$$yVersión publicada
000084729 8564_ $$s111417$$uhttps://zaguan.unizar.es/record/84729/files/texto_completo.jpg?subformat=icon$$xicon$$yVersión publicada
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000084729 951__ $$a2024-01-22-15:33:03
000084729 980__ $$aARTICLE