Inexact A-Proximal Point Algorithm and Applications to Nonlinear Variational Inclusion Problems

R. P. Agarwal () and R. U. Verma ()
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R. P. Agarwal: Florida Institute of Technology
R. U. Verma: International Publications (USA)

Journal of Optimization Theory and Applications, 2010, vol. 144, issue 3, No 1, 444 pages

Abstract: Abstract A generalization to the Rockafellar theorem (1976) on the linear convergence in the context of approximating a solution to a general class of inclusion problems involving set-valued A-maximal relaxed monotone mappings using the proximal point algorithm in a real Hilbert space setting is given. There exists a vast literature on this theorem, but most of the investigations are focused on relaxing the proximal point algorithm and applying it to the inclusion problems. The general framework for A-maximal relaxed monotonicity generalizes the theory of set-valued maximal monotone mappings, including H-maximal monotone mappings. The obtained results are general in nature, while application-oriented as well.

Keywords: Inclusion problems; Maximal monotone mapping; A-maximal relaxed monotone mapping; Generalized resolvent operator (search for similar items in EconPapers)
Date: 2010
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DOI: 10.1007/s10957-009-9615-3

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