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dc.contributor.author
Lotito, Pablo Andres
dc.contributor.author
Parente, Lisandro Armando
dc.contributor.author
Solodov, M.
dc.date.available
2022-11-02T02:18:35Z
dc.date.issued
2008-12
dc.identifier.citation
Lotito, Pablo Andres; Parente, Lisandro Armando; Solodov, M.; A Class of Variable Metric Decomposition Methods for Monotone Variational Inclusions; Heldermann Verlag; Journal of Convex Analysis; 16; 12-2008; 857-880
dc.identifier.issn
0944-6532
dc.identifier.uri
http://hdl.handle.net/11336/175876
dc.description.abstract
We extend the general decomposition scheme of [32], which is based on the hybrid inexact proximal point method of [38], to allow the use of variable metric in subproblems, along the lines of [23]. We show that the new general scheme includes as special cases the splitting method for composite mappings [25] and the proximal alternating directions method [13, 17] (in addition to the decomposition methods of [10, 42] that were already covered by [32]). Apart from giving a unified insight into the decomposition methods in question and openning the possibility of using variable metric, which is a computationally important issue, this development also provides linear rate of convergence results not previously available for splitting of composite mappings and for the proximal alternating directions methods. [10] X. Chen and M. Teboulle. A proximal-based decomposition method for convex minimization problems. Mathematical Programming, 64:81–101, 1994.Mathematical Programming, 64:81–101, 1994. [13] J. Eckstein. Some saddle-function splitting methods for convex programming. Optimization Methods and Software, 4:75–83, 1994. [17] B. He, L.Z. Liao, D. Han and H. Yang. A new inexact alternating directions method for monotone variational inequalities. Mathematical Programming, 92:103–118, 2002.Mathematical Programming, 92:103–118, 2002. [23] L.A. Parente, P.A. Lotito and M.V. Solodov. A class of inexact variable metric proximal point algorithms. SIAM Journal on Optimization, 19:240–260, 2008. [25] T. Pennanen. A splitting method for composite mappings. [25] T. Pennanen. A splitting method for composite mappings. Numerical Functional Analysis and Optimization, 23:875–890, 2002. [25] T. Pennanen. A splitting method for composite mappings. [25] T. Pennanen. A splitting method for composite mappings. Numerical Functional Analysis and Optimization, 23:875–890, 2002. SIAM Journal on Optimization, 19:240–260, 2008. [25] T. Pennanen. A splitting method for composite mappings. [25] T. Pennanen. A splitting method for composite mappings. Numerical Functional Analysis and Optimization, 23:875–890, 2002. [25] T. Pennanen. A splitting method for composite mappings. Numerical Functional Analysis and Optimization, 23:875–890, 2002. [32] M.V. Solodov. A class of decomposition methods for convex optimization and monotone variational inclusions via the hybrid inexact proximal point framework. Optimization Methods and Software, 19:557–575, 2004.Optimization Methods and Software, 19:557–575, 2004. [38] M.V. Solodov and B.F. Svaiter. A unified framework for some inexact proximal point algorithms. Numerical Functional Analysis and Optimization, 22:1013–1035, 2001.Numerical Functional Analysis and Optimization, 22:1013–1035, 2001. [42] P. Tseng. Alternating projection-proximal methods for convex programming and variational inequalities. SIAM Journal on Optimization, 7:951–965, 1997.SIAM Journal on Optimization, 7:951–965, 1997.
dc.format
application/pdf
dc.language.iso
eng
dc.publisher
Heldermann Verlag
dc.rights
info:eu-repo/semantics/openAccess
dc.rights.uri
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.subject
PROXIMAL POINT METHODS
dc.subject
VARIABLE METRIC
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SPLITTING DECOMPOSITION
dc.subject
VARIATIONAL INCLUSION
dc.subject.classification
Matemática Aplicada
dc.subject.classification
Matemáticas
dc.subject.classification
CIENCIAS NATURALES Y EXACTAS
dc.title
A Class of Variable Metric Decomposition Methods for Monotone Variational Inclusions
dc.type
info:eu-repo/semantics/article
dc.type
info:ar-repo/semantics/artículo
dc.type
info:eu-repo/semantics/publishedVersion
dc.date.updated
2021-06-07T16:58:46Z
dc.identifier.eissn
2363-6394
dc.journal.volume
16
dc.journal.pagination
857-880
dc.journal.pais
Alemania
dc.description.fil
Fil: Lotito, Pablo Andres. Universidad Nacional del Centro de la Provincia de Buenos Aires. Facultad de Ciencias Exactas. Grupo de Plasmas Densos Magnetizados. Provincia de Buenos Aires. Gobernación. Comisión de Investigaciones Científicas. Grupo de Plasmas Densos Magnetizados; Argentina. Universidad Nacional del Centro de la Provincia de Buenos Aires. Facultad de Ciencias Exactas. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
dc.description.fil
Fil: Parente, Lisandro Armando. Universidad Nacional de Rosario. Facultad de Ciencias Exactas Ingeniería y Agrimensura. Escuela de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
dc.description.fil
Fil: Solodov, M.. Instituto de Matemática Pura e Aplicada; Brasil
dc.journal.title
Journal of Convex Analysis
dc.relation.alternativeid
info:eu-repo/semantics/altIdentifier/url/https://pages.cs.wisc.edu/~solodov/lps08decomp.pdf
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