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Philip Starr Wolfe

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Profiles in Operations Research

Part of the book series: International Series in Operations Research & Management Science ((ISOR,volume 147))

Abstract

In the early 1950s, even though there were few university departments of operations research(OR), some students found the subject attractive due to the influence of a faculty advisor, specific work experience, or the intellectual challenges OR presented. In Phil Wolfe’s case, all played a role.

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References

  • Brent R, Winograd S, Wolfe P (1973) Optimal iterative processes for rootfinding. Numerische Mathematik 20:327–341

    Article  Google Scholar 

  • Cottle R, Goldfarb D, Hoffman A (eds) (1993) Festschrift in honor of Philip Wolfe. Math Program 62(1), 62(3)

    Google Scholar 

  • Dantzig G (1963) Linear programming and extensions. Princeton University Press, Princeton, NJ

    Google Scholar 

  • Dantzig G, Orden A, Wolfe P (1954) The generalized simplex method for minimizing a linear form under linear inequality constraints. The RAND Corporation, Research memorandum RM-1264, April; also, 1955, Pac J Math 5(2):183–195

    Google Scholar 

  • Dantzig G, Wolfe P (1960) Decomposition principle for linear programs. Oper Res 8(1):101–111

    Article  Google Scholar 

  • Ford L Jr, Fulkerson D (1958) A suggested computation for maximal multicommodity network flows. Manage Sci 5(1):97–101

    Article  Google Scholar 

  • Fourier J (1826) Solution d’une question particulière du calcul des inégalités. Bulletin des Sciences par la Société Philomatique, Paris 99-100, Oeuvres 2, pp 315–319

    Google Scholar 

  • Fourier J (1827) (Extract from) Analyse des travaux de l’Académie Royale des Sciences, pendant l’année 1824. Partie mathématique. Histoire l’Académie Royale des Sciences 7:xlvii–lv

    Google Scholar 

  • Frank M, Wolfe P (1956) An algorithm for quadratic programming. Nav Res Logistics Q 3(1 and 2):95–110

    Article  Google Scholar 

  • Gale D, Stewart F (1953) Infinite games with perfect information. In: Kuhn H, Tucker A (eds) Contributions to the theory of games, vol II. Annals of Mathematics Studies Number 28. Princeton University Press, Princeton, NJ, pp 245–266

    Google Scholar 

  • Gilmore P, Gomory R (1961) A linear programming approach to the cutting stock problem. Oper Res 9(6):849–859

    Article  Google Scholar 

  • Gilmore P, Gomory R (1963) A linear programming approach to the cutting stock problem -- part II. Oper Res 11(6):863–888

    Article  Google Scholar 

  • Gomory R (1958) Outline of an algorithm for integer solutions to linear programs. Bull Am Math Soc 64(5):1958

    Article  Google Scholar 

  • Gomory R (1963) An algorithm for integer solutions to linear programs. In: Graves R, Wolfe P (eds) Recent advances in mathematical programming. McGraw Hill, New York, NY, pp 269–302

    Google Scholar 

  • Grattan-Guinness I (1970) Joseph Fourier’s anticipation of linear programming. Oper Res Q 21(3):361–364

    Article  Google Scholar 

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

    Google Scholar 

  • Hoffman A (1953) Cycling in the simplex method. National Bureau of Standards Report, No. 2874, December 16, Washington, DC

    Google Scholar 

  • Khachiyan LG (1979) A polynomial algorithm in linear programming (in Russian). Doklady Akedamii Nauk SSR 244:1093–1096. [English translation: 1979. Soviet Mathematics Doklady 20:191–194]

    Google Scholar 

  • Locke E (1949) The Finan-seer. Astounding Science Fiction (October)

    Google Scholar 

  • Lustig I (2001)Interview with Phil Wolfe (text and video). http://www.e-optimization.com/directory/trailblazers/wolfe. Accessed 2 Oct 2010

  • Mapstone R (1972) Interview with Philip Wolfe. Computer oral history collection, 1969–1973, 1977. Archives Center, Smithsonian National Museum of American History, Washington, DC. http://invention.smithsonian.org/downloads/fa_cohc_tr_wolf721128.pdf. Accessed 6 May 2009)

    Google Scholar 

  • Markowitz H (1956) The optimization of a quadratic function subject to linear constraints. Nav Res Logistics Q 3(1 and 2):111–133

    Article  Google Scholar 

  • Micchelli CA (ed) (2003) Selected papers of Alan J. Hoffman with commentary. World Scientific, River Edge, NJ

    Google Scholar 

  • New York Times (1979) A Soviet discovery rocks world of mathematics. November 7, 1

    Google Scholar 

  • Sion M, Wolfe P (1957) On a game without a value. In: Dresher M, Tucker A, Wolfe P (eds) Contributions to the theory of games, vol III. Annals of Mathematics Studies Number 39. Princeton University Press, Princeton, NJ, pp 299–306

    Google Scholar 

  • Spielberg K (2007) IP over 40+ years at IBM scientific centers and marketing. Ann Oper Res 149(1):195–208

    Article  Google Scholar 

  • Von Neumann J, Morgenstern O (1944) Theory of games and economic behavior. Princeton University Press, Princeton, NJ (2nd edn, 1947; 3rd edn, 1953)

    Google Scholar 

  • Wolfe P (1956) Determinateness of polyhedral games. In: Kuhn H, Tucker A (eds) Linear inequalities and related systems. Annals of Mathematics Studies Number 38. Princeton University Press, Princeton, NJ, pp 195–198

    Google Scholar 

  • Wolfe P (1961) Accelerating the cutting plane method for nonlinear programming. J Soc Ind Appl Math 9(3):481–488

    Article  Google Scholar 

  • Wolfe P (1963a) A technique for resolving degeneracy in linear programming. J Soc Ind Appl Math 11(2):205–211

    Article  Google Scholar 

  • Wolfe P (1963b) Methods of nonlinear programming. In: Graves R, Wolfe P (eds) Recent advances in mathematical programming. McGraw-Hill, New York, NY, pp 67–86

    Google Scholar 

  • Wolfe P (1966) On the convergence of gradient methods under constraints. Report RZ-204. IBM T. J. Watson Research Center, Yorktown Heights, New York, NY

    Google Scholar 

  • Wolfe P (1967) Methods of nonlinear programming. In: Abadie J (ed) Nonlinear programming. North-Holland, Amsterdam, pp 97–131

    Google Scholar 

  • Wolfe P (1969) Convergence conditions for ascent methods. SIAM Rev 11(2):226–235

    Article  Google Scholar 

  • Wolfe P (1970) Convergence theory in non-linear programming. In: Abadie J (ed) Integer and non-linear programming. North Holland, Amsterdam, pp 1–36

    Google Scholar 

  • Wolfe P (1971) Convergence conditions for ascent methods, II: some corrections. SIAM Rev 13(2):185–188

    Article  Google Scholar 

  • Wolfe P (1974) Note on a method of conjugate subgradients for minimizing nondifferentiable functions. Math Program 7(1):380–383

    Article  Google Scholar 

  • Wolfe P (2009) Personal communication

    Google Scholar 

  • Wolfe P, Cutler L (1963) Experiments in linear programming. In: Graves R, Wolfe P (1963) (eds) Recent advances in mathematical programming. McGraw-Hill, New York, NY, pp 177–200

    Google Scholar 

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Acknowledgments

In preparing this profile, I have been aided by correspondence with Andrew Conn, Richard Cottle, and, especially, Phil Wolfe.

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Authors and Affiliations

  1. IBM,  ,  

    Alan J. Hoffman

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  1. Alan J. Hoffman
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  1. , School of Management, University at Buffalo, State University, Jacobs Management Center 160, Buffalo, 14260-4000, New York, USA

    Arjang A. Assad

  2. Robert H. Smith School of Business, University of Maryland, Van Munching Hall, College Park, 20742-1915, Maryland, USA

    Saul I. Gass

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Hoffman, A.J. (2011). Philip Starr Wolfe. In: Assad, A., Gass, S. (eds) Profiles in Operations Research. International Series in Operations Research & Management Science, vol 147. Springer, Boston, MA. https://doi.org/10.1007/978-1-4419-6281-2_34

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