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Programmes in Paired Spaces

Published online by Cambridge University Press:  20 November 2018

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The basic problem of linear programming is to minimize (or maximize) a linear function of a finite number of variables constrained by a finite number of linear inequalities. From a mathematical point of view the subject may be regarded as being divided into two areas. One is primarily analytical and deals with certain questions of duality and consistency. The other is algorithmic and is concerned with computational questions and methods.

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 1961

References

1. Arrow, K. J., Karlin, S., and Scarf, H., Studies in the mathematical theory of inventory and production (Stanford, 1958).Google Scholar
2. Bellman, R., Dynamic programming (Princeton, 1957).Google Scholar
3. Bourbaki, N., Espaces vectoriels topologiques (Eléments de Mathématique, XV, Première Partie (Paris, 1953]), V, chapters I and II.Google Scholar
4. Bourbaki, N., Espaces vectoriels topologiques (Eléments de Mathématique, XVIII, Première Partie [Paris, 1955]), V, chapters III, IV, and V.Google Scholar
5. Bratton, D., The duality theorem in linear programming, Cowles Commission Discussion Papers, Mathematics No. 427 (1955).Google Scholar
6. Charnes, A., Cooper, W. W., and Henderson, A., Introduction to linear programming (New- York, 1953).Google Scholar
7. Chernoff, H. and Reiter, S., Selection of a distribution function to minimize an expectation subject to side conditions, Technical Report No. 23, Applied Mathematics and Statistics Laboratory, Stanford University (1954).Google Scholar
8. Dantzig, G. B., The programming of interdependent activities: mathematical model, in (20) 1932.Google Scholar
9. Dantzig, G. B., Maximization of a linear function of variables subject to linear inequalities, in (20) 339347.Google Scholar
10. Duffin, R. J., Infinite programs, in (23) 157170.Google Scholar
11. Dunford, N. and Schwartz, J. T., Linear operators, Part I: General theory (New York, 1958).Google Scholar
12. Gale, D., Kuhn, H. W., and Tucker, A. W., Linear programming and theory of games, in (20) 317329.Google Scholar
13. Gass, Saul I., Linear programming: methods and applications (New York, 1958).Google Scholar
14. Haar, A., Ueber lineare Ungleichungen, Acta Math. (Szeged), 2 (1924-26), 114.Google Scholar
15. Hurwicz, L., Programming in linear spaces in K. J. Arrow, L. Hurwicz, and H. Uzawa, Studies in linear and non-linear programming (Stanford, 1958) 38102.Google Scholar
16. Isaacson, S. and Rubin, H., On minimizing an expectation subject to certain side conditions, Technical Report No. 25, Applied Mathematics and Statistics Laboratory, Stanford University (1954).Google Scholar
17. University of Kansas, Linear topological spaces (1953).Google Scholar
18. Kantorovitch, L., On the translocation of masses, Comptes Rendus (Doklady) de l'Académie des Sciences de l'URSS, XXXVII (1942), 7-8. Reproduced in Management Science 5 (1958), 14.Google Scholar
19. Khamis, S. H., On the reduced moment problem, Ann. Math. Stat., 22 (1951), 532536.Google Scholar
20. Koopmans, T. C. (ed.), Activity analysis of production and allocation (New York, 1951).Google Scholar
21. Koopmans, T. C., Three essays on the state of economic science (New York, 1957).Google Scholar
22. Kretschmer, K. S., Linear programming in locally convex spaces and its use in analysis (Dissertation, Carnegie Institute of Technology, June, 1958).Google Scholar
23. Kuhn, H. W. and Tucker, A. W. (eds.), Linear inequalities and related systems (Princeton, 1956).Google Scholar
24. Sherman Lehman, R., On the continuous simplex method, The Rand Corporation, Research Memorandum RM-1386 (1954).Google Scholar