Skip to main content
SpringerLink
Log in

George B. Dantzig: a legendary life in mathematical programming

  • Published:
Mathematical Programming Submit manuscript

Abstract

Mathematical programming owes much to George B. Dantzig who passed away on May 13, 2005 at the age of 90. This article is a tribute to this legendary pioneer and a very brief review of his extensive and enduring contributions to our field.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Albers, D.J., Reid, C.: An interview with George B. Dantzig: The father of linear programming. College Mathematics Journal 17, 292–314 (1986). [The same interview appears in D.J. Albers, G.J. Alexanderson, C. Reid (eds.), More Mathematical People: Contemporary Conversations. Boston: Harcourt Brace Jovanovich, 1990.]

    MathSciNet  Google Scholar 

  2. Dantzig, G.B. et al.: On the need for a system (sic) optimization laboratory. In: T.C. Hu, S.M. Robinson (eds.), Mathematical Programming New York: Academic Press, 1973. [See also, G.B. Dantzig, On the need for a systems optimization laboratory. In R.W. Cottle, J. Krarup (eds.), Optimisation Methods, London: The English Universities Press, 1974.]

  3. Cottle, R.W.: The Basic George B. Dantzig. Stanford, California: Stanford University Press, 2003. 1970, pp. 79–90

  4. Dantzig, G.B.: On the non-existence of tests of ``Student's'' hypothesis having power functions independent of sigma. Ann. Math. Stat. 11, 186–192 (1940)

    MATH  MathSciNet  Google Scholar 

  5. Dantzig, G.B.: I Complete Form of the Neyman-Pearson Lemma; II On the Non-Existence of Tests of ``Student's'' Hypothesis having Power Functions Independent of Sigma. Doctoral dissertation, Department of Mathematics, University of California at Berkeley, 1946

  6. Dantzig, G.B.: Programming in a linear structure. Econometrica 17, 73–74 (1949)

    Google Scholar 

  7. Dantzig, G.B.: Upper bounds, secondary constraints, and block triangularity in linear programming. Econometrica 23, 174–183 (1955)

    MATH  MathSciNet  Google Scholar 

  8. Dantzig, G.B.: Linear programming under uncertainty. Management Science 1, 197–206 (1955)

    MATH  MathSciNet  Google Scholar 

  9. Dantzig, G.B.: On the shortest route through a network. Management Science 6, 187–190 (1960)

    MATH  MathSciNet  Google Scholar 

  10. Dantzig, G.B.: On the significance of solving linear programs with some integer variables. Econometrica 28, 30–44 (1960)

    MATH  MathSciNet  Google Scholar 

  11. Dantzig, G.B.: Linear Programming and Extensions. Princeton, N.J.: Princeton University Press, 1963

  12. Dantzig, G.B.: Reminiscences about the origins of linear programming. Oper. Res. Lett. 1, 43–48 (1982)

    Article  MathSciNet  Google Scholar 

  13. Dantzig, G.B.: Reminiscences about the origins of linear programming. In: A. Bachem, M. Grötschel, B. Korte (eds.), Mathematical Programming: The State of the Art, Berlin: Springer-Verlag, 1983

  14. Dantzig, G.B.: Reminiscences about the origins of linear programming. In: R.W. Cottle, M.L. Kelmanson, B. Korte (eds.), Mathematical Programming. [Proceedings of the International Congress on Mathematical Programming, Rio de Janeiro, Brazil, 6–8 April, 1981]. Amsterdam: North-Holland, 1984

  15. Dantzig, G.B.: Linear programming. In: J.K. Lenstra et al. (eds.), History of Mathematics, Amsterdam: CWI and North-Holland, 1991

  16. Dantzig, G.B., Fulkerson, D.R.: Minimizing the number of tankers to meet a fixed schedule. Naval Research Logistics Quarterly 1, 217–222 (1954)

    Google Scholar 

  17. Dantzig, G.B., Fulkerson, D.R.: On the max-flow min-cut theorem of networks. In: H.W. Kuhn, A.W. Tucker (eds.), Linear Inequalities and Related Systems. Princeton: Princeton University Press, 1956

  18. Dantzig, G.B., Fulkerson, D.R., Johnson, S.: Solution of a large-scale traveling-salesman problem. J. Oper. Res. Soc. America 2, 393–410 (1954)

    MathSciNet  Google Scholar 

  19. Dantzig, G.B., Madansky, A.: On the solution of two-staged linear programs under uncertainty. In: J. Neyman (ed.), Proceedings of the Fourth Berkeley Symposium on Mathematical Statistics and Probability, Volume I, Theory of Statistics, Berkeley: University of California Press, 1961

  20. Dantzig, G.B., McAllister, P.H., Stone, J.C.: Formulating an objective for an economy. Math. Program. Series B 42, 11–32 (1988)

    MATH  MathSciNet  Google Scholar 

  21. Dantzig, G.B., Orden, A., Wolfe, P.: The generalized simplex method for minimizing a linear form under linear inequality constraints. Pacific J. Math. 5, 183–195 (1955)

    MATH  MathSciNet  Google Scholar 

  22. Dantzig, G.B., Saaty, T.L.: Compact City. San Francisco: Freeman, 1973

  23. Dantzig, G.B., Thapa, M.N.: Linear Programming 1: Introduction. New York: Springer, 1997

  24. Dantzig, G.B., Thapa, M.N.: Linear Programming 2: Theory and Extensions. New York: Springer, 2003

  25. Dantzig, G.B., Wald, A.: On the fundamental lemma of Neyman and Pearson. Ann. Math. Stat. 22, 87–93 (1951)

    MATH  MathSciNet  Google Scholar 

  26. Dantzig, G.B., Wolfe, P.: Decomposition principle for linear programs. Oper. Res. 8, 101–111 (1960)

    Article  MATH  Google Scholar 

  27. Dantzig, G.B., Wolfe, P.: The decomposition algorithm for linear programming. Econometrica 29, 767–778 (1961)

    MATH  MathSciNet  Google Scholar 

  28. Dantzig, T.: Number, The Language of Science, New York: Macmillan, 1930

  29. Hitchcock, F.L.: The distribution of a product from several sources to numerous localities. J. Math. Phys. 20, 224–230 (1941)

    MATH  MathSciNet  Google Scholar 

  30. Koopmans, T.C. ed.: Activity Analysis of Production and Allocation. New York: John Wiley & Sons, 1951

  31. Leontief, W.: The Structure of the American Economy. New York: Oxford University Press, 1951

  32. Tucker, A.W.: Dual systems of homogeneous linear relations. In: H.W. Kuhn, A.W. Tucker (eds.), Linear Inequalities and Related Systems. [Annals of Mathematics Study 38.] Princeton, N.J.: Princeton University Press, 1956

Download references

Author information

Authors and Affiliations

  1. Dept. of Management Sciences and Engineering, Terman Engineering Center, Stanford University, Stanford, CA, 94305-4026, USA

    Richard W. Cottle

Authors
  1. Richard W. Cottle
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Cottle, R. George B. Dantzig: a legendary life in mathematical programming. Math. Program. 105, 1–8 (2006). https://doi.org/10.1007/s10107-005-0674-4

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10107-005-0674-4

Keywords

Search

Navigation