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Relatively Inexact Proximal Point Algorithm and Linear Convergence Analysis
Author
Source
International Journal of Mathematics and Mathematical Sciences
Issue
Vol. 2009, Issue 2009 (31 Dec. 2009), pp.1-11, 11 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2009-11-22
Country of Publication
Egypt
No. of Pages
11
Main Subjects
Abstract EN
Based on a notion of relatively maximal (m)-relaxed monotonicity, the approximation solvability of a general class of inclusion problems is discussed, while generalizing Rockafellar's theorem (1976) on linear convergence using the proximal point algorithm in a real Hilbert space setting.
Convergence analysis, based on this new model, is simpler and compact than that of the celebrated technique of Rockafellar in which the Lipschitz continuity at 0 of the inverse of the set-valued mapping is applied.
Furthermore, it can be used to generalize the Yosida approximation, which, in turn, can be applied to first-order evolution equations as well as evolution inclusions.
American Psychological Association (APA)
Verma, Ram U.. 2009. Relatively Inexact Proximal Point Algorithm and Linear Convergence Analysis. International Journal of Mathematics and Mathematical Sciences،Vol. 2009, no. 2009, pp.1-11.
https://search.emarefa.net/detail/BIM-490966
Modern Language Association (MLA)
Verma, Ram U.. Relatively Inexact Proximal Point Algorithm and Linear Convergence Analysis. International Journal of Mathematics and Mathematical Sciences No. 2009 (2009), pp.1-11.
https://search.emarefa.net/detail/BIM-490966
American Medical Association (AMA)
Verma, Ram U.. Relatively Inexact Proximal Point Algorithm and Linear Convergence Analysis. International Journal of Mathematics and Mathematical Sciences. 2009. Vol. 2009, no. 2009, pp.1-11.
https://search.emarefa.net/detail/BIM-490966
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-490966