Super-Relaxed Open image in new window-Proximal Point Algorithms, Relaxed Open image in new window-Proximal Point Algorithms, Linear Convergence Analysis, and Nonlinear Variational InclusionsReport as inadecuate




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Fixed Point Theory and Applications

, 2009:957407

First Online: 27 September 2009Received: 26 June 2009Accepted: 30 August 2009

Abstract

We glance at recent advances to the general theory of maximal set-valued monotone mappings and their role demonstrated to examine the convex programming and closely related field of nonlinear variational inequalities. We focus mostly on applications of the super-relaxed Open image in new window-proximal point algorithm to the context of solving a class of nonlinear variational inclusion problems, based on the notion of maximal Open image in new window-monotonicity. Investigations highlighted in this communication are greatly influenced by the celebrated work of Rockafellar 1976, while others have played a significant part as well in generalizing the proximal point algorithm considered by Rockafellar 1976 to the case of the relaxed proximal point algorithm by Eckstein and Bertsekas 1992. Even for the linear convergence analysis for the overrelaxed or super-relaxed Open image in new window-proximal point algorithm, the fundamental model for Rockafellar-s case does the job. Furthermore, we attempt to explore possibilities of generalizing the Yosida regularization-approximation in light of maximal Open image in new window-monotonicity, and then applying to first-order evolution equations-inclusions.

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Author: Ravi P. Agarwal - Ram U. Verma

Source: https://link.springer.com/







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