Evolution equations for maximal monotone operators: asymptotic analysis in continuous and discrete time
By Juan Peypouquet, Sylvain Sorin. 2009
156 citations recorded by the source corpus.
This survey is devoted to the asymptotic behavior of solutions of evolution equations generated by maximal monotone operators in Hilbert spaces. The emphasis is in the comparison of the continuous time trajectories to sequences generated by implicit or explicit discrete time schemes. The analysis covers weak convergence for the average process, for the process itself and strong convergence and aims at highlighting the main ideas and unifying the proofs. We further make the connection with the analysis in terms of almost orbits that allows for a broader scope.
Subfields: Computational Theory and Mathematics, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/ef733351ce474f2f9084d7e00e3adce0f941a968
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In Computational Theory and Mathematics
In Mathematical Physics
Citations in the corpus
- Rate of convergence of the Nesterov accelerated gradient method in the subcritical case α ≤ 3 (2017, background): “One can consult [11], [29], [30], [31] for a recent account on the proximal-based splitting methods.”
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- ARock: an Algorithmic Framework for Asynchronous Parallel Coordinate Updates (2015, background): “weak convergence follows from Opial’s Lemma [49, 44] and Lemma 3.”