Relatively Inexact Proximal Point Algorithm and Linear Convergence Analysis

Ram U. Verma

International Journal of Mathematics and Mathematical Sciences, 2009, vol. 2009, 1-11

Abstract:

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.

Date: 2009
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:691952

DOI: 10.1155/2009/691952

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