Generalization of accelerated successive projection method for convex sets intersection problems

Seyed Rasoul Etesami, Angelia Nedich, Tamer Basar

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

We consider a successive projection method for finding a common point in the intersection of closed convex sets with a nonempty interior. We first generalize an iterative projection algorithm known as acceleration method that was introduced earlier in [1] from the case of two closed convex sets to a finite number of closed convex sets, assuming that the intersection set has a nonempty interior. In particular, we establish the convergence of such an algorithm to a common feasible point in the intersection of all the sets. Following this, we establish a geometric rate of convergence for the generalized method when we restrict the convex sets to the class of half-spaces in finite dimensional Euclidean spaces.

Original languageEnglish (US)
Title of host publication2016 American Control Conference, ACC 2016
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages4422-4427
Number of pages6
Volume2016-July
ISBN (Electronic)9781467386821
DOIs
StatePublished - Jul 28 2016
Externally publishedYes
Event2016 American Control Conference, ACC 2016 - Boston, United States
Duration: Jul 6 2016Jul 8 2016

Other

Other2016 American Control Conference, ACC 2016
CountryUnited States
CityBoston
Period7/6/167/8/16

Keywords

  • Acceleration method
  • Closed convex sets
  • Convergence rate
  • Half-spaces
  • Successive projection

ASJC Scopus subject areas

  • Electrical and Electronic Engineering

Cite this

Etesami, S. R., Nedich, A., & Basar, T. (2016). Generalization of accelerated successive projection method for convex sets intersection problems. In 2016 American Control Conference, ACC 2016 (Vol. 2016-July, pp. 4422-4427). [7525618] Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/ACC.2016.7525618