Monotone (nonlinear) operators in Hilbert space

By G. Minty. 1962

Subfields: Mathematical Optimization, Numerical Methods & Scientific Computing

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Citations in the corpus

A Tight and Unified Analysis of Extragradient for a Whole Spectrum of Differentiable Games (2019, neutral): “For v monotone (Minty, 1962; Rockafellar, 1976), the proximal point operator can be deﬁned as P η ( ω ) = (Id + ηv ) − 1 ( ω ) for ω ∈ R d .”
An Inertial Forward-Backward Algorithm for Monotone Inclusions (2014, background): “In case, T is a general monotone operator, the classical algorithm to solve (1) is the proximal point algorithm which can be traced back to the early works of Minty [31] and Martinet [30].”
Local mapping relations and global implicit function theorems (1969, unknown): “, Browder [1] and Minty [11]).”
Five lectures on optimal transportation: Geometry, regularity and applications (2010, methodology): “[102] George J. Minty.”
Tight global linear convergence rate bounds for Douglas–Rachford splitting (2015, background): “The resolvent has full domain since A is assumed maximally monotone, see [26] and [3, Proposition 23.”
Well-posedness of stochastic partial differential equations with fully local monotone coefficients (2022, methodology): “The theory of monotone operators was initiated in the fundamental work of Minty [29], and then studied systematically by Browder, and later developed by Leray and Lions, Hartman and Stampacchia, We refer the reader to [21, 44] for a detailed exposition.”
Two-scale convergence of some integral functionals (2007, background): “We confine ourselves to single-valued functions, although after [25,31,39] one may expect that these results take over to multi-valued functions (that are the most natural framework for maximal monotonicity).”
A Stochastic forward-backward splitting method for solving monotone inclusions in Hilbert spaces (2014, background): “Maximal monotone operators have been extensively studied since [37], largely because they have wide applications in pure and applied sciences, and because they provide a convenient framework for a unified treatment of equilibrium problems, variational inequalities, and convex optimization, see [5, 5”
Fitzpatrick functions, cyclic monotonicity and Rockafellar's antiderivative (2007, background): “1 reduces to Minty’s theorem [32] which states that a monotone operator A is maximal monotone if and only if Id +A is surjective, i.”
A Primer on Monotone Operator Methods (2015, background): “That domR = domC = R, called the Minty surjectivity theorem [89], is harder to show, and we skip the proof.”
Generalized finite-difference schemes (1969, background): “Thus, Gic) is a monotone operator in the sense of Minty [9].”
Proximal Algorithms (2013, background): “, the classical work of Brézis [37], Browder [39, 38, 40, 41], Minty [139, 140], Kachurovskii [111, 112], and Rockafellar [171, 170], as well as Eckstein’s thesis [78] and the recent monograph by Bauschke and Combettes [10].”