Set-valued mappings and enlargements of monotone operators

By Regina Sandra Burachik, Alfredo Noel Iusem. 2008

308 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics, Geometry and Topology, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/df98d610f445eede4eef9eb3167872de66a66b7d

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In Computational Theory and Mathematics

In Geometry and Topology

In Numerical Analysis

Citations in the corpus

Inexact Proximal Point Methods for Equilibrium Problems in Banach Spaces (2007, unknown): “7 of [6] for the case of g (x) = (1/2)‖x‖2, = 1.”
On the proximal point method for equilibrium problems in Hilbert spaces (2010, background): “7 in [2], which also deals with Banach spaces.”
A Hybrid Proximal-Extragradient Algorithm with Inertial Effects (2014, background): “Introduced in [13], this notion proved to possess fruitful properties in connection with the theory of monotone operators [11, 12, 14], being used also in the formulation of several numerical schemes of proximal-type.”
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].”
Weak and Strong Convergence of Algorithms for the Split Common Null Point Problem (2011, methodology): “Then, for the general case, we employ a product space formulation in order to transform the SCNPP into an SCFPP, in a similar fashion to what has been done in [23, Section 4] and [20, Subsection 6.1].”
The Split Common Null Point Problem (2011, background): “For more details on many of the notions and results quoted here see, e.g., the recent books [4, 10].”
Proximal Algorithms (2013, background): “Building on Rockafellar’s work, there is a substantial literature studying the proximal point algorithm in the monotone operator setting; this is closely connected to the literature on set-valued mappings, fixed point theory, nonexpansive mappings, and variational inequalities [202, 37, 103, 175, 81”
On the Maximal Monotonicity of Diagonal Subdifferential Operators (2010, methodology): “5 in [3]), but we include a proof of this fact, which is quite elementary, for the sake of self-containment, and also because we will use part of it later on.”