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

MSC:
90C55Methods of successive quadratic programming type
65G30Interval and finite arithmetic
90C25Convex programming
References:
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[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.
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[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.
[12]Rockafellar, R. T.,Convex Analysis, Princeton University Press, Princeton, New Jersey, 1970.
[13]Stoer, J., andWitzgall, C.,Convexity and Optimization in Finite Dimensions, I, Springer-Verlag, Berlin, Germany, 1970.
[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.
[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.