Evolution equations for maximal monotone operators: asymptotic analysis in continuous and discrete time

Details Evolution equations for maximal monotone operators: asymptotic analysis in continuous and discrete time Evolution equations for maximal monotone operators: asymptotic analysis in continuous and discrete time

2009-05-08

arxiv.org/abs/0905.1270v1

Mathematics

Optimization and Control

45 pages

Scientific paper

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.

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