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Variational Sum of Monotone Operators
, 1994
"... this paper to the case of maximal monotone operators A and B. Indeed, as pointed out in the following simple example, although the sum of two maximal monotone operators is a monotone operator, it may fail to be a maximal monotone operator. Define the linear operator A by ..."
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Cited by 12 (4 self)
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this paper to the case of maximal monotone operators A and B. Indeed, as pointed out in the following simple example, although the sum of two maximal monotone operators is a monotone operator, it may fail to be a maximal monotone operator. Define the linear operator A by
On the DouglasRachford splitting method and the proximal point algorithm for maximal monotone operators
, 1992
"... ..."
MULTISCALE HOMOGENIZATION OF MONOTONE OPERATORS
"... (Communicated by Giuseppe Buttazzo) Abstract. In this paper we prove a generalization of the iterated homogenization theorem for monotone operators, proved by Lions et al. in [20] and [21]. Our results enable us to homogenize more realistic models of multiscale structures. 1. Introduction. In ..."
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Cited by 2 (1 self)
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(Communicated by Giuseppe Buttazzo) Abstract. In this paper we prove a generalization of the iterated homogenization theorem for monotone operators, proved by Lions et al. in [20] and [21]. Our results enable us to homogenize more realistic models of multiscale structures. 1. Introduction. In
Lectures on maximal monotone operators
 Extracta Mathematicae
, 1997
"... Introduction. These lectures will focus on those properties of maximal monotone operators which are valid in arbitrary real Banach spaces. Most applications (to nonlinear partial differential equations, optimization, calculus of variations, etc.) take place in reflexive spaces, in part because sever ..."
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Cited by 14 (0 self)
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Introduction. These lectures will focus on those properties of maximal monotone operators which are valid in arbitrary real Banach spaces. Most applications (to nonlinear partial differential equations, optimization, calculus of variations, etc.) take place in reflexive spaces, in part because
Monotone Operations and Monotone Groups
"... We survey an algebraic approach to proving impossibility results in distributed computing. ..."
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We survey an algebraic approach to proving impossibility results in distributed computing.
CAPACITY THEORY FOR MONOTONE OPERATORS
, 1995
"... If Au = −div(a(x, Du)) is a monotone operator defined on the Sobolev space W 1,p (R n), 1 < p < +∞, with a(x, 0) = 0 for a.e. x ∈ R n, the capacity CA(E, F) relative to A can be defined for every pair (E, F) of bounded sets in R n with E ⊂ F. We prove that CA(E, F) is increasing and countably ..."
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Cited by 1 (0 self)
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If Au = −div(a(x, Du)) is a monotone operator defined on the Sobolev space W 1,p (R n), 1 < p < +∞, with a(x, 0) = 0 for a.e. x ∈ R n, the capacity CA(E, F) relative to A can be defined for every pair (E, F) of bounded sets in R n with E ⊂ F. We prove that CA(E, F) is increasing
Asplund Decompositions of Monotone Operators
 Control, SetValued Analysis & Applications, CSVAA
, 2004
"... Abstract. We establish representations of a monotone mapping as the sum of a maximal subdifferential mapping and a ‘remainder ’ monotone mapping, where the remainder is either skew linear, or more broadly ‘acyclic’, in the sense that it contains no nontrivial subdifferential component. Examples are ..."
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Cited by 9 (3 self)
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Abstract. We establish representations of a monotone mapping as the sum of a maximal subdifferential mapping and a ‘remainder ’ monotone mapping, where the remainder is either skew linear, or more broadly ‘acyclic’, in the sense that it contains no nontrivial subdifferential component. Examples
Recent progress on Monotone Operator Theory
, 2012
"... In this paper, we survey recent progress on the theory of maximally monotone operators in general Banach space. We also extend various of the results and leave some open questions. ..."
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Cited by 10 (4 self)
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In this paper, we survey recent progress on the theory of maximally monotone operators in general Banach space. We also extend various of the results and leave some open questions.
Results 1  10
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323,179