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

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  • R. P. Agarwal

    (Florida Institute of Technology)

  • R. U. Verma

    (International Publications (USA))

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.

Suggested Citation

  • R. P. Agarwal & R. U. Verma, 2010. "Inexact A-Proximal Point Algorithm and Applications to Nonlinear Variational Inclusion Problems," Journal of Optimization Theory and Applications, Springer, vol. 144(3), pages 431-444, March.
    • Handle: RePEc:spr:joptap:v:144:y:2010:i:3:d:10.1007_s10957-009-9615-3
    DOI: 10.1007/s10957-009-9615-3
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    References listed on IDEAS

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    1. R. T. Rockafellar, 1976. "Augmented Lagrangians and Applications of the Proximal Point Algorithm in Convex Programming," Mathematics of Operations Research, INFORMS, vol. 1(2), pages 97-116, May.
    2. R. U. Verma, 2004. "Generalized System for Relaxed Cocoercive Variational Inequalities and Projection Methods," Journal of Optimization Theory and Applications, Springer, vol. 121(1), pages 203-210, April.
    3. R. U. Verma, 2006. "A-Monotonicity and Its Role in Nonlinear Variational Inclusions," Journal of Optimization Theory and Applications, Springer, vol. 129(3), pages 457-467, June.
    4. R. U. Verma, 2006. "General System of A-Monotone Nonlinear Variational Inclusion Problems with Applications," Journal of Optimization Theory and Applications, Springer, vol. 131(1), pages 151-157, October.
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