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A Characterization of Maximal Monotone Operators
Set-Valued Analysis, 2007It is shown that a set-valued map M : R q R q is maximal monotone if and only if the following five conditions are satisfied: (i) M is monotone; (ii) M has a nearly convex domain; (iii) M is convex-valued; (iv) the recession cone of the values M(x) equals the normal cone to the closure of the domain of M at x; (v) M has a closed graph.
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About the Maximal Monotonicity of the Generalized Sum of Two Maximal Monotone Operators
Set-Valued and Variational Analysis, 2011We give several regularity conditions, both closedness and interior point type, that ensure the maximal monotonicity of the generalized sum of two strongly-representable monotone operators, and we extend some recent results concerning on the same problem.
Szilárd László +1 more
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On the Maximality of the Sum of Two Maximal Monotone Operators
2018Let E be a real reflexive Banach space, E∗ be the dual space of E and \(T: D(T)\subseteq E\to 2^{E^{*}}\), \(S:D(S)\subseteq E\to 2^{E^*}\) be two maximal monotone operators such that D(T) ∩ D(S) ≠ ∅. Assume that there exist x0 ∈ E, r > 0, λ0 > 0 such that inff ∈ Tx(f, x − x0) is lower bounded on each bounded subset of D(T) and, if, for each y ∈ B(x0 ...
Themistocles M. Rassias +2 more
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On the maximality of the sum of two maximal monotone operators
Nonlinear Analysis: Theory, Methods & Applications, 1981Abstract : A wide variety of problems involving nonlinear partial differential equations, subject to boundary conditions, may be shown to have solutions by establishing that the associated differential operators satisfy a certain technical condition. This condition, called maximal monotonicity, allows the use of a well developed abstract theory which ...
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Coderivatives of Maximal Monotone Operators
2018In this chapter we employ the tools of variational analysis and generalized differentiation developed above to study global and local monotonicity of set-valued operators.
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Cyclical monotonicity of maximal monotone step operators
Boletim da Sociedade Brasileira de Matemática, 1982Maximal monotone operatorsT:X→2y such that {Tx} xex is a finite family of sets are shown to be cyclically monotone.
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Bundle Methods for Maximal Monotone Operators [PDF]
, 1999 To find a zero of a maximal monotone operator T we use an enlargement T e playing the role of the e-subdifferential in nonsmooth optimization. We define a convergent and implementable algorithm which combines projection ideas with bundle-like techniques and a transportation formula.
Benar Fux Svaiter +2 more
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Maximal Hyperclones Determined by Monotone Operations
2011 41st IEEE International Symposium on Multiple-Valued Logic, 2011Let A be a finite set. It is well known that every bounded partial order relation determines a maximal clone on A and every non-trivial partial order relation determines a maximal partial clone on A. In this paper we describe a class of maximal hyper clones that are determined by bounded partial order relations on A.
Jelena Colic +2 more
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Perturbations of regularizing maximal monotone operators
Israel Journal of Mathematics, 1982We consideru′(t)+Au(t)∋f(t), whereA is maximal monotone in a Hilbert spaceH.
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