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Role of Relative A-Maximal Monotonicity in Overrelaxed Proximal-Point Algorithms with Applications

Author

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  • R. P. Agarwal

    (Florida Institute of Technology)

  • R. U. Verma

    (International Publications)

Abstract

A general framework for a class of overrelaxed proximal point algorithms based on the notion of relative A-maximal monotonicity is introduced; then, the convergence analysis for solving a general class of nonlinear variational inclusion problems is explored. The framework developed in this communication is quite suitable, unlike other existing notions of generalized maximal monotonicity, including A-maximal (m)-relaxed monotonicity in literature, to generalize first-order nonlinear evolution equations/evolution inclusions based on the generalized nonlinear Yosida approximations in Hilbert spaces as well as in Banach spaces.

Suggested Citation

  • R. P. Agarwal & R. U. Verma, 2009. "Role of Relative A-Maximal Monotonicity in Overrelaxed Proximal-Point Algorithms with Applications," Journal of Optimization Theory and Applications, Springer, vol. 143(1), pages 1-15, October.
    • Handle: RePEc:spr:joptap:v:143:y:2009:i:1:d:10.1007_s10957-009-9554-z
    DOI: 10.1007/s10957-009-9554-z
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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, 2006. "A-Monotonicity and Its Role in Nonlinear Variational Inclusions," Journal of Optimization Theory and Applications, Springer, vol. 129(3), pages 457-467, June.
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