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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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Representable Monotone Operators and Limits of Sequences of Maximal Monotone Operators [PDF]
Set-Valued and Variational Analysis, 2011 We show that the lower limit of a sequence of maximal monotone operators on a reflexive Banach space is a representable monotone operator. As a consequence, we obtain that the variational sum of maximal monotone operators and the variational composition of a maximal monotone operator with a linear continuous operator are both representable monotone ...
Marc Lassonde
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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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Maximality of the Sum of a Maximally Monotone Linear Relation and a Maximally Monotone Operator [PDF]
Set-Valued and Variational Analysis, 2013 16 pages.
Borwein, Jonathan M., Yao, Liangjin
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Finite difference schemes with monotone operators
Advances in Difference Equations, 2004 Several existence theorems are given for some second-order difference equations associated with maximal monotone operators in Hilbert spaces. Boundary conditions of monotone type are attached.
N. C. Apreutesei
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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
Jean-Christophe Pesquet +3 more
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Fixed Point Theory and Applications, 2009 We prove strong convergence theorems for finding a common element of the zero point set of a maximal monotone operator and the fixed point set of a hemirelatively nonexpansive mapping in a Banach space by using monotone hybrid iteration method.
Chakkrid Klin-eam, Suthep Suantai
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On the maximal monotonicity and the range of the sum of nonlinear maximal monotone operators [PDF]
Proceedings of the Edinburgh Mathematical Society, 1991 Conditions are given on two maximal monotone (multivalued) operators A and B which ensure that A + B is also maximal. One condition used is that ∥Bx∥≦k(∥x∥)Ax| +d|(A + B)x| + c(∥x∥) for every x∈D(A)⊆D(B), where 0≦k(r)<1, and c(r)≧0 are nondecreasing functions, and 0≦d≦1 is a constant. Here, for a set C, |C| denotes inf{∥y∥:y∈C}.
Webb, J. R. L., Zhao, Weiyu
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Journal of Inequalities and Applications, 2018 In this paper, we present two iterative algorithms for approximating a solution of the split feasibility problem on zeros of a sum of monotone operators and fixed points of a finite family of nonexpansive mappings.
Narin Petrot +2 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, 2011 15 pages ...
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