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Báo cáo hóa học: " Review Article Super-Relaxed (η)-Proximal Point Algorithms, Relaxed (η)-Proximal Point Algorithms, Linear Convergence Analysis, and Nonlinear Variational Inclusions"

Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: Review Article Super-Relaxed (η)-Proximal Point Algorithms, Relaxed (η)-Proximal Point Algorithms, Linear Convergence Analysis, and Nonlinear Variational Inclusions | Hindawi Publishing Corporation Fixed Point Theory and Applications Volume 2009 Article ID 957407 47 pages doi 10.1155 2009 957407 Review Article Super-Relaxed n -Proximal Point Algorithms Relaxed n -Proximal Point Algorithms Linear Convergence Analysis and Nonlinear Variational Inclusions Ravi P. Agarwal1 2 and Ram U. Verma1 3 1 Department of Mathematical Sciences Florida Institute of Technology Melbourne FL 32901 USA 2 Department of Mathematics and Statistics King Fahd University of Petroleum and Minerals Dhahran 31261 Saudi Arabia 3 International Publications USA 12085 Lake Cypress Circle Suite I109 Orlando FL 32828 USA Correspondence should be addressed to Ravi P. Agarwal agarwal@fit.edu Received 26 June 2009 Accepted 30 August 2009 Recommended by Lai Jiu Lin 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 n -proximal point algorithm to the context of solving a class of nonlinear variational inclusion problems based on the notion of maximal n -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 n -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 n -monotonicity and then applying to first-order evolution equations inclusions. Copyright 2009 R. P. Agarwal and R. U. Verma. This is an open access article distributed under the .