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Mathematics, 2020 This paper is devoted to the study of evolution problems involving fractional flow and time and state dependent maximal monotone operator which is absolutely continuous in variation with respect to the Vladimirov’s pseudo distance.
Charles Castaing +2 more
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The sum of a maximal monotone operator of type (FPV) and a maximal monotone operator with full domai [PDF]
Nonlinear Analysis: Theory, Methods & Applications, 2010 The most important open problem in Monotone Operator Theory concerns the maximal monotonicity of the sum of two maximal monotone operators provided that Rockafellar's constraint qualification holds. In this paper, we prove the maximal monotonicity of $A+
Liangjin Yao
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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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Differential-algebraic inclusions with maximal monotone operators [PDF]
2016 IEEE 55th Conference on Decision and Control (CDC), 2016 The term differential-algebraic inclusions (DAIs) not only describes the dynamical relations using set-valued mappings, but also includes the static algebraic inclusions, and this paper considers the problem of existence of solutions for a class of such dynamical systems described by the inclusion equation for a symmetric positive semi-definite matrix ...
M. Camlibel +3 more
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Abstract and Applied Analysis, 2010 We introduce a new hybrid iterative scheme for finding a common element of the set of common fixed points of two countable families of relatively quasi-nonexpansive mappings, the set of the variational inequality for an α-inverse-strongly monotone ...
Siwaporn Saewan, Poom Kumam
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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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Fixed Point Theory and Applications, 2009 We introduce an iterative scheme for finding a common element of the solution set of a maximal monotone operator and the solution set of the variational inequality problem for an inverse strongly-monotone operator in a uniformly smooth and uniformly ...
Somyot Plubtieng, Wanna Sriprad
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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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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 ...
García, Yboon, Lassonde, Marc
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Càdlàg Skorokhod problem driven by a maximal monotone operator [PDF]
, 2013 The article deals with the existence and uniqueness of the solution of the following differential equation (a cadlag Skorokhod problem) driven by a maximal monotone operator, and with singular input generated by the cadlag function m : { d x t + A ( x t )
Lucian Maticiuc +3 more
semanticscholar +1 more source