Discrete approximations and fixed set iterations in Banach spaces

Tzanko Donchev, Elza Farkhi, Simeon Reich

Research output: Contribution to journalArticlepeer-review

Abstract

We study autonomous differential inclusions with right-hand sides satisfying a onesided Lipschitz (OSL) condition in Banach spaces with uniformly convex duals. We first show that the solution set is closed and obtain estimates for Euler-type discrete approximations. We then use these results to derive an analogue of the exponential formula for the reachable set, as well as results regarding the existence and approximation of a strongly invariant attractor in the case of a negative OSL constant. As a by-product, conditions for controllability of the reverse-time system are obtained.

Original languageEnglish
Pages (from-to)895-906
Number of pages12
JournalSIAM Journal on Optimization
Volume18
Issue number3
DOIs
StatePublished - 2007

Keywords

  • Banach space
  • Differential inclusion
  • Duality mapping
  • Euler approximations
  • Exponential formula
  • Fixed set iterations
  • One-sided Lipschitz condition
  • Upper hemicontinuous

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