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

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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.

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Authors and Affiliations

  1. Mathematical Sciences, Florida Institute of Technology, Melbourne, FL, 32901, USA

    R. P. Agarwal

  2. International Publications (USA), Orlando, FL, 32828, USA

    R. U. Verma

Authors
  1. R. P. Agarwal
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  2. R. U. Verma
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Correspondence to R. P. Agarwal.

Additional information

Communicated by F. Potra.

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Agarwal, R.P., Verma, R.U. Inexact A-Proximal Point Algorithm and Applications to Nonlinear Variational Inclusion Problems. J Optim Theory Appl 144, 431–444 (2010). https://doi.org/10.1007/s10957-009-9615-3

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  • DOI: https://doi.org/10.1007/s10957-009-9615-3

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