From Hahn-Banach to monotonicity

By Stephen Simons. 2008

319 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/8631df864b963e33744b85d1a0937148755a4f1a

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In Applied Mathematics

In Computational Theory and Mathematics

In Numerical Analysis

Citations in the corpus

Fixed-Point Algorithms for Inverse Problems in Science and Engineering (2011, background): “are believed to play a role in the analysis of algorithms featuring resolvents when the sum of the underlying maximal monotone operators is not maximal, and Simons considered generalizations of maximal monotonicity to more abstract settings [84], nowadays called Simons or SSD spaces.”
Firmly Nonexpansive Mappings and Maximally Monotone Operators: Correspondence and Duality (2011, unknown): “, the books [5], [6], [7], [9], [22], [23], [24], [26], [27], and [28].”
Convex Functions: Constructions, Characterizations and Counterexamples (2010, background): “Such results extend to closed linear operators [396], and many are subsumed or much clarified by [6].”
Inertial Douglas-Rachford splitting for monotone inclusion problems (2014, methodology): “We recall first some notations used in the variational case, see [6, 8, 9, 24, 35, 37].”
Forward-Backward and Tseng’s Type Penalty Schemes for Monotone Inclusion Problems (2013, methodology): “For the reader’s convenience we present first some notations which are used throughout the paper (see [4, 7, 8, 16, 22, 25]).”
Regularity conditions via generalized interiority notions in convex optimization: New achievements and their relation to some classical statements (2009, background): “We refer to [8,13,14,42] for several examples showing that in general the implications above are strict.”
A Hybrid Proximal-Extragradient Algorithm with Inertial Effects (2014, unknown): “For the notions and results presented as follows we refer the reader to [5–7, 12, 16, 24].”
A Dynamical System Associated with the Fixed Points Set of a Nonexpansive Operator (2014, background): “For readers convenience let us recall some standard notions and results in monotone operator theory which will be used in the following (see also [6, 8, 22]).”