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

90C55Methods of successive quadratic programming type
65G30Interval and finite arithmetic
90C25Convex programming
Full Text: DOI
[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.
[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.