Evolution Equations for Maximal Monotone Operators: Asymptotic Analysis in Continuous and Discrete Time

Juan Peypouquet*, Sylvain Sorin

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review

55 Citations (Scopus)

Abstract

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 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. The aim is to highlight the main ideas and unifying the proofs. Furthermore the connection is made with the analysis in terms of almost orbits that allows for a broader scope.

Original languageEnglish
Pages (from-to)1113-1163
Number of pages51
JournalJournal of Convex Analysis
Volume17
Issue number3-4
Publication statusPublished - 2010
Externally publishedYes

Keywords

  • WEAK-CONVERGENCE THEOREMS
  • PROXIMAL POINT ALGORITHM
  • HILBERT-SPACE
  • BANACH-SPACES
  • CONTRACTION-SEMIGROUPS
  • NONEXPANSIVE-MAPPINGS
  • NONLINEAR SEMIGROUPS
  • CONVEX MINIMIZATION
  • SEMI-GROUPS
  • BEHAVIOR

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