TY - GEN

T1 - Generalization of accelerated successive projection method for convex sets intersection problems

AU - Etesami, Seyed Rasoul

AU - Nedic, Angelia

AU - Basar, Tamer

N1 - 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:
© 2016 American Automatic Control Council (AACC).

PY - 2016/7/28

Y1 - 2016/7/28

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

UR - http://www.scopus.com/inward/record.url?scp=84992153675&partnerID=8YFLogxK

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U2 - 10.1109/ACC.2016.7525618

DO - 10.1109/ACC.2016.7525618

M3 - Conference contribution

AN - SCOPUS:84992153675

T3 - Proceedings of the American Control Conference

SP - 4422

EP - 4427

BT - 2016 American Control Conference, ACC 2016

PB - Institute of Electrical and Electronics Engineers Inc.

T2 - 2016 American Control Conference, ACC 2016

Y2 - 6 July 2016 through 8 July 2016

ER -