Analysis of the convergence rate for the cyclic projection algorithm applied to basic semialgebraic convex sets

Title: Analysis of the convergence rate for the cyclic projection algorithm applied to basic semialgebraic convex sets
Creator: Borwein, Jonathan M.; Li, Guoyin; Yao, Liangjin
Relation: ARC
Relation: Siam Journal on Optimization Vol. 24, Issue 1, p. 498-527
Publisher Link: http://dx.doi.org/10.1137/130919052
Publisher: Society for Industrial and Applied Mathematics (SIAM)
Resource Type: journal article
Date: 2014
Description: In this paper, we study the rate of convergence of the cyclic projection algorithm applied to finitely many basic semialgebraic convex sets. We establish an explicit convergence rate estimate which relies on the maximum degree of the polynomials that generate the basic semialgebraic convex sets and the dimension of the underlying space. We achieve our results by exploiting the algebraic structure of the basic semialgebraic convex sets.
Subject: cyclic projection algorithm; convex polynomial; distance function; Fejér monotone sequence; Hölderian regularity; Lojasiewicz's inequality; projector operator; basic semialgerbraic convex set; von Neumann alternating projection method
Identifier: http://hdl.handle.net/1959.13/1302342
Identifier: uon:20458
Identifier: ISSN:1052-6234
Language: eng
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