Remote Access Bulletin of the American Mathematical Society

Bulletin of the American Mathematical Society

ISSN 1088-9485(online) ISSN 0273-0979(print)

 

 

On the intersections of cones and subspaces


Authors: A. Ben-Israel and A. Charnes
Journal: Bull. Amer. Math. Soc. 74 (1968), 541-544
DOI: https://doi.org/10.1090/S0002-9904-1968-12000-2
MathSciNet review: 0232183
Full-text PDF Free Access

References | Additional Information

References [Enhancements On Off] (What's this?)

  • 1. Adi Ben-Israel, Notes on linear inequalities. I. The intersection of the nonnegative orthant with complementary orthogonal subspaces, J. Math. Anal. Appl. 9 (1964), 303–314. MR 0168368, https://doi.org/10.1016/0022-247X(64)90045-9
  • 2. A. Ben-Israel and A. Charnes, Contributions to the theory of generalized inverses, J. Soc. Indust. Appl. Math. 11 (1963), 667–699. MR 0179192
  • 3. C. C. Braunschweiger and H. E. Clark, An Extension of the Farkas Theorem, Amer. Math. Monthly 69 (1962), no. 4, 272–277. MR 1531625, https://doi.org/10.2307/2312940
  • 4. C. C. Braunschweiger, An Extension of the Nonhomogeneous Farkas Theorem, Amer. Math. Monthly 69 (1962), no. 10, 969–975. MR 1531934, https://doi.org/10.2307/2313191
  • 5. N. Bourbaki, Eléments de mathématique. XV. Première partie: Les structures fondamentales de l’analyse. Livre V: Espaces vectoriels topologiques. Chapitre I: Espaces vectoriels topologiques sur un corps valué. Chapitre II: Ensembles convexes et espaces localement convexes, Actualités Sci. Ind., no. 1189, Herman & Cie, Paris, 1953 (French). MR 0054161
  • 6. A. Charnes and W. W. Cooper, Management models and industrial applications of linear programming, John Wiley & Sons, Inc., New York-London, 1961. MR 0157773
    A. Charnes and W. W. Cooper, Management models and industrial applications of linear programming. Vol. II, John Wiley & Sons, Inc., New York-London, 1961. MR 0157774
  • 7. Ky Fan, On systems of linear inequalities, Linear inequalities and related systems, Annals of Mathematics Studies, no. 38, Princeton University Press, Princeton, N.J., 1956, pp. 99–156. MR 0087901
  • 8. K. Fan, Convex sets and their applications, Argonne National Laboratory Lecture notes, Argonne, Ill., summer 1959.
  • 9. J. Farkas, Über die Theorie der einfachen Ungleichungen, J. Reine Angew. Math. 124 (1902), 1-24.
  • 10. A. J. Goldman and A. W. Tucker, Polyhedral convex cones, Linear equalities and related systems, Annals of Mathematics Studies, no. 38, Princeton University Press, Princeton, N. J., 1956, pp. 19–40. MR 0087974
  • 11. L Hurwicz, "Programming in linear spaces, " Chapter 4 in: K. J. Arrow, L. Hurwicz and J. Uzawa, Studies in linear and nonlinear programming, Stanford Univ. Press, Stanford, Calif., 1958.
  • 12. H. W. Kuhn and A. W. Tucker (Editors), Linear inequalities and related systems, Princeton Univ. Press, Princeton, N. J., 1956.
  • 13. Norman Levinson, Linear programming in complex space, J. Math. Anal. Appl. 14 (1966), 44–62. MR 0225569, https://doi.org/10.1016/0022-247X(66)90061-8
  • 14. N. Levinson and T. O. Sherman, The sum of the intersections of a cone with a linear subspace and of dual cone with orthogonal complementary subspace, J. Combinatorial Theory 1 (1966), 338–349. MR 0205047
  • 15. T. S. Motzkin, Beiträge zur Theorie der linearen Ungleichungen (Dissertation, Basel, 1933) Azriel, Jerusalem, 1936.
  • 16. R. Penrose, A generalized inverse for matrices, Proc. Cambridge Philos. Soc. 51 (1955), 406–413. MR 0069793
  • 17. Angus E. Taylor, Introduction to functional analysis, John Wiley & Sons, Inc., New York; Chapman & Hall, Ltd., London, 1958. MR 0098966
  • 18. A. W. Tucker, Dual systems of homogeneous linear relations, Linear inequalities and related systems, Annals of Mathematics Studies, no. 38, University Press, Princeton, N. J., 1956, pp. 3–18. MR 0089112


Additional Information

DOI: https://doi.org/10.1090/S0002-9904-1968-12000-2