Results 11 to 20 of about 25,465 (308)
Maximality of the sum of a maximally monotone linear relation and a maximally monotone operator [PDF]
Set-Valued and Variational Analysis, 2012 The most famous open problem in Monotone Operator Theory concerns the maximal monotonicity of the sum of two maximally monotone operators provided that Rockafellar's constraint qualification holds. In this paper, we prove the maximal monotonicity of $A+
Borwein, Jonathan M., Yao, Liangjin
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Maximal monotone operators with non-maximal graphical limit
Examples and Counterexamples, 2022 We present a counterexample showing that the graphical limit of maximally monotone operators might not be maximally monotone. We also characterize the directional differentiability of the resolvent of an operator B in terms of existence and maximal ...
Gerd Wachsmuth
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Nonlinear Maximal Monotone Extensions of Symmetric Operators [PDF]
Journal of Evolution Equations, 2015 Given a linear semi-bounded symmetric operator $S\ge -\omega$, we explicitly define, and provide their nonlinear resolvents, nonlinear maximal monotone operators $A_\Theta$ of type $\lambda>\omega$ (i.e.
Posilicano, Andrea
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Complete Closedness of Maximal Monotone Operators [PDF]
Mathematics of Operations Research, 1983 (This paper is dedicated to the memory of Professor Kwan Chao-Chin, former academic member and director of the Institute of System Science of the Academy of Chinese Sciences.) A maximal monotone operator in Rn is completely closed, i.e., not only closed for points, but also closed for directions. Such a completely closed operator is locally bounded at
Liqun Qi
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Approximating Iterations for Nonexpansive and Maximal Monotone Operators [PDF]
Abstract and Applied Analysis, 2015 We present two algorithms for finding a zero of the sum of two monotone operators and a fixed point of a nonexpansive operator in Hilbert spaces. We show that these two algorithms converge strongly to the minimum norm common element of the zero of the ...
Zhangsong Yao +3 more
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The sum of a maximal monotone operator of type (FPV) and a maximal monotone operator with full domain is maximal monotone [PDF]
Nonlinear Analysis: Theory, Methods & Applications, 2010 15 pages ...
Liangjin Yao
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Eigenvalue results for pseudomonotone perturbations of maximal monotone operators [PDF]
Open Mathematics, 2013 Kim In-Sook, Bae Jung-Hyun
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Fixed Point Theory and Applications, 2008 We introduce a new hybrid iterative algorithm for finding a common element of the set of fixed points of hemirelatively nonexpansive mappings and the set of solutions of an equilibrium problem and for finding a common element of the set of zero points ...
Cheng Yun, Tian Ming
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Composite iterative schemes for maximal monotone operators in reflexive Banach spaces
Fixed Point Theory and Applications, 2011 In this article, we introduce composite iterative schemes for finding a zero point of a finite family of maximal monotone operators in a reflexive Banach space. Then, we prove strong convergence theorems by using a shrinking projection method.
Cho Yeol +2 more
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Learning Maximally Monotone Operators for Image Recovery [PDF]
SIAM Journal on Imaging Sciences, 2021 We introduce a new paradigm for solving regularized variational problems. These are typically formulated to address ill-posed inverse problems encountered in signal and image processing. The objective function is traditionally defined by adding a regularization function to a data fit term, which is subsequently minimized by using iterative optimization
Pesquet, Jean-Christophe +3 more
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