Nothing Special   »   [go: up one dir, main page]

Skip to main content
Log in

Cyclic subgradient projections

  • Short Communication
  • Published:
Mathematical Programming Submit manuscript

Abstract

A cyclically controlled method of subgradient projections (CSP) for the convex feasibility problem of solving convex inequalities is presented. The features of this method make it an efficient tool in handling huge and sparse problems. A particular application to an image reconstruction problem of emission computerized tomography is mentioned.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

References

  1. R. Aharoni, A. Berman and Y. Censor, “An interior points algorithm for the convex feasibility problem”,Advances in Applied Mathematics, to appear.

  2. Y. Censor, D. Gustafson, A. Lent and H. Tuy, “A new approach to the emission computerized tomography problem: Calculating attenuation and concentration coefficients simultaneously”,IEEE Transactions on Nuclear Science NS-26 (1979) 2775–2779.

    Google Scholar 

  3. Y. Censor and A. Lent, “A cyclic subgradient projections method for the convex feasibility problem”, Technical Report, Department of Mathematics, University of Haifa (July, 1980).

  4. Y. Censor, “Iterative methods for the convex feasibility problem”,Annals of Discrete Mathematics, to appear.

  5. I.I. Eremin, “On some iterative methods in convex programming”,Ekonomika i Matematichesky Methody 2 (1966) 870–886. [In Russian.]

    Google Scholar 

  6. L.G. Gubin, B.T. Polyak and E.V. Raik, “The method of projections for finding the common point of convex sets”,USSR Computational Mathematics and Mathematical Physics 7 (1967) 1–24.

    Google Scholar 

  7. W. Oettli, “Symmetric duality, and a convergent subgradient method for discrete, linear, constrained approximation problems with arbitrary norms appearing in the objective function and in the constraints”,Journal of Approximation Theory 14 (1975) 43–50.

    Google Scholar 

  8. E. Raik, “Fejer's type methods in Hilbert space”,Izvestija Akademii Nauk Estonskoy SSR 16 (1967) 286–293. [In Russian.]

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

Research supported by National Institute of Health Grant HL 28438-01.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Censor, Y., Lent, A. Cyclic subgradient projections. Mathematical Programming 24, 233–235 (1982). https://doi.org/10.1007/BF01585107

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01585107

Key words

Navigation