Brief Biography
Philip Starr Wolfe was born in San Francisco, and during his childhood lived in several California cities. He was an excellent student in elementary school and loved science, but foundered on algebra and geometry in high school, until he read Euclid's axioms and early theorems, at which point, he said, he and Euclid "became colleagues."
He entered the University of California at Berkeley (UCB) in 1943 but withdrew and was drafted into the US Army shortly before the end of the war. He had various assignments, the last of which was to teach German to intelligence operatives for work in Germany. In 1947 he returned to UCB and completed undergraduate, Masters, and PhD degrees. In the course of his PhD studies he learned from a science fiction article of the existence of game theory, and aimed at writing his dissertation on the subject.
This interest led to an internship with George Dantzig at the Air Force’s Project SCOOP (Scientific Computation of Optimal Programs) in the Pentagon. Dantzig challenged Wolfe to find a way to resolve the problem that could be encountered by Dantzig's simplex algorithm for computing solutions to linear programming (LP) problems, which proceeded from vertex to vertex of a polyhedron determined by the constraints of the LP. Wolfe did so, with the idea of using lexicographical ordering to distinguish among the possibly multiple algebraic characterizations of a vertex that can give rise to cycling. Wolfe's dissertation included both this approach and original work in game theory.
Wolfe received his PhD from the UCB in 1954 and accepted a position at Princeton University. His Princeton research focused quadratic programming, the constrained maximization or minimization of a quadratic function. With Marguerite Frank, he developed a computational procedure for quadratic programming that was published in the same issue of the Naval Research Logistics Quarterly as a related paper by Harry Markowitz on portfolio selection by parametric quadratic minimization. At Princeton Wolfe developed an interest in computing, helped administer the Princeton Logistics Research Project, taught calculus and game theory, developed a procedure for solving quadratic programs that required only minor modifications in a simplex algorithm computer code, and interacted with many distinguished visitors.
Before joining Princeton, Wolfe had been offered a higherpaid position at RAND, which he turned down. But in 1957 RAND doubled their earlier offer and Wolfe went back to California, where he was assigned to RAND's computing group. There he was associated with George Dantzig, Ray Fulkerson, and Lloyd Shapley, and worked on ways to improve the simplex algorithm. In particular, with George Dantzig he developed a decomposition method to solve linear programming problems that had only a few constraints linking variables of several smaller LP problems and, for other problems, to generate LP matrix columns as they were needed in the computation.
In 1964, his friend Ralph Gomory, who was Director of Mathematical Sciences at IBM's T. J. Watson Research Laboratory in Yorktown Heights, NY, arranged a 6month sabbatical for Wolfe at IBM's Zurich research lab, and later hired him for a regular position at Yorktown. He remained there for the rmainder of his career.
When Wolfe arrived at IBM, the Research division had no group specifically focused on optimization. As it soon became evidence that such a team was needed, Gomory selected Wolfe to lead it. Though he had administrative responsibilities, Wolfe continued his work on nonlinear programming. He published many important articles on nondifferential and constrained optimization as well as convergence theory. In 1970 he started the journal Mathematical Programming and helped found and later served as chairman of the Mathematical Programming Society.
In 1992, Wolfe and his friend Alan Hoffman were awarded the John von Neumann Theory Prize by ORSA and TIMS. They were recognized for their contributions to the intellectual foundations of mathematical programming. In presenting the prize, George Nemhauser lauded Wolfe for the sixtyplus papers on mathematical programming that he published. Wolfe served as an adjunct professor at Columbia University and, following his retirement in 1996, taught courses at the New York Polytechnic Institute, Columbia University, and City University of New York.
Other Biographies
Profiles in Operations Research:
Philip Wolfe
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Education
University of California, Berkeley, A.B. 1948
University of California, Berkeley, MA 1950
University of California, Berkeley, PhD 1954 (Mathematics Genealogy)
Affiliations
Academic Affiliations
 Columbia University
 New York University (Polytechnic Institute of Brooklyn)
 Princeton University
 University of California, Berkeley
 City University of New York
NonAcademic Affiliations
Key Interests in OR/MS
Methodologies
Application Areas
Oral Histories
Philip Wolfe Interview by Irv Lustig, May 4, 2001. Video by Irv Lustig, Short Hills, NJ.
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Philip Wolfe (1972) Interview by Robina Mapstone, November 28. Lemelson Center for the Study of Invention and Innovation, Smithsonian National Museum of American History. (transcript)
Awards and Honors
John Von Neumann Theory Prize 1992
Mathematical Programming Society's Founders Award 2000
The Institute for Operations Research and the Management Sciences Fellow 2002
Professional Service
Mathematical Programming Society, Chairman 197880
Selected Publications
Dantzig G. B., Orden A., & Wolfe P. (1955). The generalized simplex method for minimizing a linear form under linear inequality restraints. Pacific Journal of Mathematics, 5 (2): 183195.
Frank M. & Wolfe P. (1956) An algorithm for quadratic programming. Naval research logistics quarterly, 3(1‐2): 95110.
Drescher M., Tucker A. W., & Wolfe P., eds. (1957) Contributions to the Theory of Games, Volume 3. Princeton University Press: Princeton, N.J.
Wolfe P. (1959) The Simplex Method for Quadratic Programming. Econometrica, 27 (3): 382398.
Wolfe P. (1966) On the convergence of gradient methods under constraint. Report RZ204. IBM T. J. Watson Research Center: York Heights, New York.
Wolfe P. (1969) Convergence conditions for ascent methods. SIAM review, 11 (2): 226235.
Wolfe P. (1970) Convergence theory in nonlinear programming. Abadie J., ed. in Integer and Nonlinear Programming: 136. North Holland: Amsterdam.
Crowder H. P., Held M., & Wolfe P. (1974) Validation of subgradient optimization. Mathematical Programming, 6 (1): 6288.
Wolfe P. (1974) Note on a method of conjugate subgradients for minimizing nondifferentiable functions. Mathematical Programming, 7 (1): 380383.
Hoffman A. J. & Wolfe P. (1985) History. Lawler E. L., Lenstra J. K., Rimmooy Kan A. H. G., & Shmoys D. B., eds. in The Traveling Salesman Problem. John Wiley & Sons: New York.
Additional Resources
Cottle R. W. (1993) Festschrift in honor of Philip Wolfe. Amsterdam: NorthHolland.