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Analysis of the Convergence Rate for the Cyclic Projection Algorithm Applied to Basic Semialgebraic Convex Sets

J.M. Borwein University of Newcastle Guoyin Li University of New South Wales Liangjin Yao University of Newcastle

Numerical Analysis and Scientific Computing Numerical Linear Algebra Optimization and Control mathscidoc:2108.25001

SIAM Journal on Optimization, 24, (1), 498–527, 2014.10
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.
cyclic projection algorithm, convex polynomial, distance function, Fejer monotone sequence, Holderian regularity, Lojasiewicz’s inequality, projector operator, basic semialgebraic convex set, von Neumann alternating projection method
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@inproceedings{j.m.2014analysis,
  title={Analysis of the Convergence Rate for the Cyclic Projection Algorithm Applied to Basic Semialgebraic Convex Sets},
  author={J.M. Borwein, Guoyin Li, and Liangjin Yao},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20210823151045440429860},
  booktitle={SIAM Journal on Optimization},
  volume={24},
  number={1},
  pages={498–527},
  year={2014},
}
J.M. Borwein, Guoyin Li, and Liangjin Yao. Analysis of the Convergence Rate for the Cyclic Projection Algorithm Applied to Basic Semialgebraic Convex Sets. 2014. Vol. 24. In SIAM Journal on Optimization. pp.498–527. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20210823151045440429860.
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