Results 11 to 20 of about 24,742 (267)
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
core +3 more sources
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
doaj +3 more sources
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
openaire +4 more sources
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
openaire +2 more sources
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
openaire +2 more sources
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 ...
Camlibel, Kanat +3 more
openaire +1 more source
Boundary of Maximal Monotone Operators Values
Applied Mathematics & Optimization, 2018 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Hantoute, Abderrahim, Nguyen, Bao Tran
openaire +3 more sources
NOTES ON GRAPH-CONVERGENCE FOR MAXIMAL MONOTONE OPERATORS [PDF]
Bulletin of the Australian Mathematical Society, 2010 AbstractWe construct a sequence {An} of maximal monotone operators with a common domain and converging, uniformly on bounded subsets, to another maximal monotone operator A; however, the sequence {t−1nAn} fails to graph-converge for some null sequence {tn}.
CIANCIARUSO, Filomena +3 more
openaire +2 more sources
Strong convergence of an iterative sequence for maximal monotone operators in a Banach space
Abstract and Applied Analysis, 2004 We first introduce a modified proximal point algorithm for maximal monotone operators in a Banach space. Next, we obtain a strong convergence theorem for resolvents of maximal monotone operators in a Banach space which generalizes the previous result by ...
Fumiaki Kohsaka, Wataru Takahashi
doaj +1 more source
Journal of Applied Mathematics, 2014 We introduce and study a class of new general systems of set-valued variational inclusions involving (A,η)-maximal relaxed monotone operators in Hilbert spaces.
Ting-jian Xiong, Heng-you Lan
doaj +1 more source