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Relatively Inexact Proximal Point Algorithm and Linear Convergence Analysis

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  • Ram U. Verma

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.

Suggested Citation

  • Ram U. Verma, 2009. "Relatively Inexact Proximal Point Algorithm and Linear Convergence Analysis," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2009, pages 1-11, November.
    • Handle: RePEc:hin:jijmms:691952
    DOI: 10.1155/2009/691952
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