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Journal of optimization theory and applications, ISSN 1573-2878, 2019, Volume 181, Issue 3, pp. 709 - 726
Journal Article
Numerical algorithms, ISSN 1572-9265, 2015, Volume 71, Issue 3, pp. 519 - 540
We introduce and investigate the convergence properties of an inertial forward-backward-forward splitting algorithm for approaching the set of zeros of the sum of a maximally monotone operator... 
Primal-dual algorithm | 65K05 | Subdifferential | Numeric Computing | Theory of Computation | Inertial splitting algorithm | Maximally monotone operator | Algorithms | Algebra | Resolvent | Convex optimization | 90C25 | Numerical Analysis | Computer Science | 47H05 | MATHEMATICS, APPLIED | PROXIMAL POINT ALGORITHM | COMPOSITE | CONVERGENCE | MAPPINGS | OPTIMIZATION | OPERATORS | Operators | Splitting | Image processing | Inertial | Inclusions | Optimization | Convergence
Journal Article
Optimization, ISSN 1029-4945, 2018, Volume 68, Issue 10, pp. 1855 - 1880
We investigate a forward-backward splitting algorithm of penalty type with inertial effects for finding the zeros of the sum of a maximally monotone operator and a cocoercive one and the convex normal... 
Maximally monotone operator | forward-backward splitting algorithm | convex bilevel optimization | Fitzpatrick function | 65K05 | forward–backward splitting algorithm | 90C25 | 47H05 | Operators (mathematics) | Algorithms | Inclusions | Convergence | Ergodic processes
Journal Article
Set-valued and variational analysis, ISSN 1877-0541, 2011, Volume 20, Issue 1, pp. 131 - 153
The notion of a firmly nonexpansive mapping is central in fixed point theory because of attractive convergence properties for iterates and the correspondence with maximally monotone operators due to Minty... 
Banach contraction | 52A41 | Proximal map | Subdifferential operator | Mathematics | Nonexpansive mapping | Geometry | Maximally monotone operator | Rectangular | Resolvent | Secondary 26B25 | Primary 47H05 | 90C25 | Analysis | Firmly nonexpansive mapping | 47H09 | Convex function | Hilbert space | Legendre function | Paramonotone | Fixed point | MATHEMATICS, APPLIED | FITZPATRICK FUNCTIONS | EXTENSION | NONLINEAR OPERATORS | CONVERGENCE
Journal Article
Set-Valued and Variational Analysis, ISSN 1877-0533, 6/2018, Volume 26, Issue 2, pp. 369 - 384
Journal Article
Journal of optimization theory and applications, ISSN 1573-2878, 2012, Volume 157, Issue 1, pp. 1 - 24
Journal Article
Set-Valued and Variational Analysis, ISSN 1877-0533, 6/2012, Volume 20, Issue 2, pp. 155 - 167
Journal Article
Journal of the Australian Mathematical Society (2001), ISSN 1446-7887, 08/2014, Volume 97, Issue 1, pp. 1 - 26
The most important open problem in monotone operator theory concerns the maximal monotonicity of the sum of two maximally monotone operators provided that the classical... 
convex set | Fitzpatrick function | operator of type (FPV) | sum problem | convex function | constraint qualification | linear relation | maximally monotone operator | monotone operator | MATHEMATICS | DOMAIN | CONVEX-SETS | Mathematics - Functional Analysis
Journal Article
Optimization Letters, ISSN 1862-4472, 1/2014, Volume 8, Issue 1, pp. 237 - 246
We provide a concise analysis about what is known regarding when the closure of the domain of a maximally monotone operator on an arbitrary real Banach space is convex... 
Fitzpatrick function | Set-valued operator | 47B65 | Mathematics | Monotone operator | Optimization | Maximally monotone operator | Computational Intelligence | Secondary 26B25 | Primary 47H05 | Nearly convex set | 47A05 | Operations Research/Decision Theory | Numerical and Computational Physics | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | MULTIFUNCTIONS | SUM
Journal Article
Numerical functional analysis and optimization, ISSN 1532-2467, 2015, Volume 36, Issue 8, pp. 951 - 963
Journal Article
Vietnam Journal of Mathematics, ISSN 2305-221X, 12/2014, Volume 42, Issue 4, pp. 451 - 465
In this paper we consider the inclusion problem involving a maximally monotone operator, a monotone and Lipschitz continuous operator, linear compositions of parallel-sum type monotone operators... 
65K05 | Fitzpatrick function | Infimal-convolution | Subdifferential | Convex minimization problem | Mathematics | Lipschitz continuous operator | Parallel-sum | Maximally monotone operator | Resolvent | 90C25 | Mathematics, general | Forward–backward–forward algorithm | Fenchel conjugate | 47H05
Journal Article
Mathematical Programming, ISSN 0025-5610, 2015, Volume 150, Issue 2, pp. 251 - 279
Journal Article
Proceedings of the American Mathematical Society, ISSN 0002-9939, 05/2020, Volume 148, Issue 5, pp. 2035 - 2044
In his recent Proceedings of the AMS paper, ``Gossez's skew linear map and its pathological maximally monotone multifunctions'', Stephen Simons proved... 
MATHEMATICS | MATHEMATICS, APPLIED | Gossez operator | Duality map | skew operator | range | Fitzpatrick-Phelps operator | maximally monotone operator
Journal Article