Bregman-legendre multidistance projection algorithms for convex feasibility and optimization

Studies in Computational Mathematics

Volumn 8, Issue C, 2001, Pages 87-99

  Byrne, Charles ^a  

^a University of Massachusetts Lowell   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 77956682929     PISSN: 1570579X     EISSN: None     Source Type: Book Series    
DOI: 10.1016/S1570-579X(01)80008-2     Document Type: Chapter

References (15)

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3. Bregman L.M. The relaxation method of finding the common point of convex sets and its application to the solution of problems in convex programming. USSR Computational Mathematics and Mathematical Physics 7 (1967) 200-217
4. Byrne C.L. Block-iterative methods for image reconstruction from projections. IEEE Transactions on Image Processing IP-5 (1996) 792-794
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6. Byrne C.L. Block-iterative Interior point optimization methods for image reconstruction from limited data. Inverse Problems 16 (2000) 1405-1419
7. C. L. Byrne and Y. Censor, Proximity function minimization using multiple Bregmanprojections, with applications to split feasibility and Kullback-Leibler distance minimization, Annals of Operations Research accepted for publication.
8. Censor Y., and Elfving T. A multiprojection algorithm using Bregman projections in a product space. Numerical Algorithms 8 (1994) 221-239
9. Censor Y., and Zenios S.A. Parallel Optimization: Theory, Algorithms and Applications (1997), Oxford University Press, New York
10. Kotzer T., Cohen N., and Shamir J. A projection-based algorithm for consistent and inconsistent constraints. SIAM J. Optim. 7 2 (1997) 527-546
11. Landweber L. An iterative formula for Fredholm integral equations of the first kinds. Amer. J. of Math. 73 (1951) 615-624
12. Lange K., Bahn M., and Little R. A theoretical study of some maximum likelihood algorithms for emission and transmission tomography. IEEE Trans. Med. Imag. 6 (1987) 106-114
13. M. Narayanan, C. L. Byrne and M. King, An interior point iterative reconstruction algorithm incorporating upper and lower bounds, with application to SPECT transmission imaging, IEEE Trans. Medical Imaging, submitted for publication.
14. Rockafellar R.T. Convex Analysis (1970), Princeton University Press, Princeton, New Jersey
15. Youla D.C. Mathematical theory of image restoration by the method of convex projections. In: Stark H. (Ed). Image Recovery: Theory and Applications (1987), Academic Press, Orlando, Florida, USA 29-78