- 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
- Full Text
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