×
Censor, Y.; Lent, A.

An iterative row-action method for interval convex programming. (English) Zbl 0431.49042

J. Optimization Theory Appl. 34, 321-353 (1981).
Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page
scan of Zbl 0431.49042

Cited in 2 Reviews
Cited in 243 Documents

MSC:

90C55 Methods of successive quadratic programming type
65G30 Interval and finite arithmetic
90C25 Convex programming

Keywords:

interval convex programming; entropy optimization; large and sparse matrices; nonorthogonal projections; image reconstruction from projections
Cite Review PDF
Full Text: DOI

References:

[1] Robers, P. D., andBen-Israel, A.,An Interval Programming Algorithm for Discrete Linear L 1-Approximation Problems, Journal of Approximation Theory, Vol. 2, pp. 323-336, 1969. · Zbl 0211.52101 · doi:10.1016/0021-9045(69)90001-X
[2] Robers, P. D., andBen-Israel, A.,A Suboptimal Method for Interval Linear Programming, Linear Algebra and Its Applications, Vol. 3, pp. 383-405, 1970. · Zbl 0215.58806 · doi:10.1016/0024-3795(70)90008-X
[3] Herman, G. T., andLent, A.,A Family of Iterative Quadratic Optimization Algorithms for Pairs of Inequalities, with Application in Diagnostic Radiology, Mathematical Programming Study, Vol. 9, pp. 15-29, 1978. · Zbl 0389.90078
[4] Herman, G. T., andLent, A.,Iterative Reconstruction Algorithms, Computers in Biology and Medicine, Vol. 6, pp. 273-294, 1976. · doi:10.1016/0010-4825(76)90066-4
[5] Herman, G. T., Lent, A., andLutz, P. H.,Relaxation Methods For Image Reconstruction, Communications of the Association for Computing Machinery, Vol. 21, pp. 152-158, 1978. · Zbl 0367.68065
[6] 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, Vol. 7, pp. 200-217, 1967. · Zbl 0186.23807 · doi:10.1016/0041-5553(67)90040-7
[7] Hildreth, C.,A Quadratic Programming Procedure, Naval Research Logistics Quarterly, Vol. 4, pp. 79-85, 1975; see alsoErratum, Naval Research Logistic Quarterly, Vol. 4, p. 361, 1975. · doi:10.1002/nav.3800040113
[8] Lent, A., andCensor, Y.,Extensions of Hildreth’s Row-Action Method for Quadratic Programming, SIAM Journal on Control and Optimization, Vol. 18, pp. 444-454, 1980. · Zbl 0444.49025 · doi:10.1137/0318033
[9] D’Esopo, D. A.,A Convex Programming Procedure, Naval Research Logistics Quarterly, Vol. 6, pp. 33-42, 1959. · doi:10.1002/nav.3800060105
[10] Censor, Y., andHerman, G. T.,Row-Generation Methods for Feasibility and Optimization Problems Involving Sparse Matrices and Their Application, Sparse Matrix Proceedings-1978, Edited by I. S. Duff and G. W. Stewart, Society for Industrial and Applied Mathematics, Philadelphia, Pennsylvania, pp. 197-219, 1979.
[11] Censor, Y.,Row-Action Methods for Huge and Sparse Systems and Their Applications, SIAM Review, to appear. · Zbl 0469.65037
[12] Rockafellar, R. T.,Convex Analysis, Princeton University Press, Princeton, New Jersey, 1970. · Zbl 0193.18401
[13] Stoer, J., andWitzgall, C.,Convexity and Optimization in Finite Dimensions, I, Springer-Verlag, Berlin, Germany, 1970. · Zbl 0203.52203
[14] Ponstein, J.,Seven Kinds of Convexity, SIAM Review, Vol. 9, pp. 115-119, 1967. · Zbl 0164.06501 · doi:10.1137/1009007
[15] Ben-Israel, A.,Linear Equations and Inequalities on Finite Dimensional, Real or Complex, Vector Spaces: A Unified Theory, Journal of Mathematical Analysis and Applications, Vol. 27, pp. 367-389, 1969. · Zbl 0174.31502 · doi:10.1016/0022-247X(69)90054-7
[16] Lent, A.,A Convergent Algorithm for Maximum Entropy Image Restoration, with a Medical X-Ray Application, Image Analysis and Evaluation, Edited by R. Shaw, Society of Photographic Scientists and Engineers, Washington, DC, pp. 249-257, 1977.
[17] Daniel, J. W.,The Approximate Minimization of Functionals, Prentice-Hall, Englewood Cliffs, New Jersey, 1971. · Zbl 0223.65014
[18] Censor, Y., Lakshminarayanan, A. V., andLent, A.,Relaxational Methods for Large-Scale Entropy Optimization Problems, with Application in Image Reconstruction, Information Linkage Between Applied Mathematics and Industry, Edited by P. C. C. Wang, Academic Press, New York, New York, pp. 539-546, 1979.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.