The asymptotic behavior of the composition of two resolvents

By Heinz H. Bauschke, Patrick L. Combettes, Simeon Reich. Nonlinear Analysis, 2005

115 citations recorded by the source corpus.

Abstract The asymptotic behavior of the composition of two resolvents in a Hilbert space is investigated. Connections are made between the solutions of associated monotone inclusion problems and their dual versions. The applications provided include a study of an alternating minimization procedure and a new proof of von Neumann's classical result on the method of alternating projections.

Subfields: Computational Theory and Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/04b4d79d9954cf327b0f8c9ef2324e9edd0253b9

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In Computational Theory and Mathematics

In Mathematical Physics

Citations in the corpus

Primal-Dual Splitting Algorithm for Solving Inclusions with Mixtures of Composite, Lipschitzian, and Parallel-Sum Type Monotone Operators (2011, background): “An important feature of the algorithm is that the Lipschitzian operators present in the formulation can be processed individually via explicit steps, while the set-valued operators are processed individually via their resolvents.”
A Dykstra-like algorithm for two monotone operators (2007, background): “(7) In [6], this duality framework proved particularly useful in the investigation of the asymptotic behavior of the composition of two resolvents.”
An inertial forward–backward splitting method for solving inclusion problems in Hilbert spaces (2018, unknown): “We note that both algorithms are weakly convergent in general [10,12,27].”
A Generalized Forward-Backward Splitting (2011, unknown): “The backward-backward algorithm [1, 7, 20, 54, 62] can be used to minimize F = g1 + g2 when the functions involved are the indicator functions of nonempty closed convex sets or involve Moreau envelopes.”
Proximal Splitting Methods in Signal Processing (2009, background): “Detailed analyses of this scheme can be found in [1,14,48,108].”
Alternating Proximal Algorithms for Weakly Coupled Minimization Problems. Applications to Dynamical Games and PDE’s (2008, background): “This kind of variational problem frequently occurs in various domains like mechanics (transmission through thin isolating layers, cracks, fissures), imaging (segmentation, image restoration), thermodynamics (phase transitions), more generally in the description of phenomena involving discontinuities”