Generalization of accelerated successive projection method for convex sets intersection problems

Seyed Rasoul Etesami; Angelia Nedic; Tamer Basar

doi:10.1109/ACC.2016.7525618

Generalization of accelerated successive projection method for convex sets intersection problems

Seyed Rasoul Etesami, Angelia Nedic, Tamer Basar

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

1 Scopus citations

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 language	English (US)
Title of host publication	2016 American Control Conference, ACC 2016
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	4422-4427
Number of pages	6
ISBN (Electronic)	9781467386821
DOIs	https://doi.org/10.1109/ACC.2016.7525618
State	Published - Jul 28 2016
Externally published	Yes
Event	2016 American Control Conference, ACC 2016 - Boston, United States Duration: Jul 6 2016 → Jul 8 2016

Publication series

Name	Proceedings of the American Control Conference
Volume	2016-July
ISSN (Print)	0743-1619

Other

Other	2016 American Control Conference, ACC 2016
Country/Territory	United States
City	Boston
Period	7/6/16 → 7/8/16

Keywords

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

ASJC Scopus subject areas

Electrical and Electronic Engineering

Access to Document

10.1109/ACC.2016.7525618

Cite this

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

Generalization of accelerated successive projection method for convex sets intersection problems. / Etesami, Seyed Rasoul; Nedic, Angelia; Basar, Tamer.

2016 American Control Conference, ACC 2016. Institute of Electrical and Electronics Engineers Inc., 2016. p. 4422-4427 7525618 (Proceedings of the American Control Conference; Vol. 2016-July).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Etesami, SR, Nedic, A & Basar, T 2016, Generalization of accelerated successive projection method for convex sets intersection problems. in 2016 American Control Conference, ACC 2016., 7525618, Proceedings of the American Control Conference, vol. 2016-July, Institute of Electrical and Electronics Engineers Inc., pp. 4422-4427, 2016 American Control Conference, ACC 2016, Boston, United States, 7/6/16. https://doi.org/10.1109/ACC.2016.7525618

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title = "Generalization of accelerated successive projection method for convex sets intersection problems",

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.",

keywords = "Acceleration method, Closed convex sets, Convergence rate, Half-spaces, Successive projection",

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note = "Funding Information: Research supported in part by the Cognitive and Algorithmic Decision Making project grant through the College of Engineering of the University of Illinois, and in part by AFOSR MURI Grant FA 9550-10-1-0573 and NSF grant CCF 11-11342 Publisher Copyright: {\textcopyright} 2016 American Automatic Control Council (AACC).; 2016 American Control Conference, ACC 2016 ; Conference date: 06-07-2016 Through 08-07-2016",

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N2 - 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.

AB - 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.

KW - Acceleration method

KW - Closed convex sets

KW - Convergence rate

KW - Half-spaces

KW - Successive projection

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Generalization of accelerated successive projection method for convex sets intersection problems

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Keywords

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