Hybrid Super-relaxed Proximal Point Algorithms and General Nonlinear Variational Inclusion Problems
نویسنده
چکیده
First a general framework for a hybrid super-relaxed proximal point algorithm based on the notion of H-maximal monotonicity is introduced, and then the convergence analysis for solving a general class of nonlinear inclusion problems is explored. The framework developed in this communication is quite suitable to generalize first-order evolution equations based on the generalized nonlinear Yosida regularization/approximation and beyond. Furthermore, the obtained results can also be applied to generalize Douglas-Rachford splitting methods for finding the zero of the sum of two generalized maximal monotone mappings. AMS Subject Classification: 49J40, 65B05
منابع مشابه
Super-Relaxed (η)-Proximal Point Algorithms, Relaxed (η)-Proximal Point Algorithms, Linear Convergence Analysis, and Nonlinear Variational Inclusions
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 η proximal point algorithm to the context of solving a class of nonlinear variational inclusion problems, based on the notion ...
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