Philip Wolfe

August 11, 1927 – December 29, 2016

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 higher-paid 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 6-month 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 sixty-plus 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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Wikipedia Entry for Philip Wolfe


University of California, Berkeley, A.B. 1948

University of California, Berkeley, MA 1950

University of California, Berkeley, PhD 1954 (Mathematics Genealogy)


Academic Affiliations
Non-Academic Affiliations

Key Interests in OR/MS

Application Areas

Oral Histories

Philip Wolfe Interview by Irv Lustig, May 4, 2001.  Video by Irv Lustig, Short Hills, NJ.

NOTE: The video chapter transcripts are searchable, with search results displayed as marks on the time bar above the search box.  Click a mark to jump to the search word or phrase in the video and transcript, or click on any word in the transcript to jump to that point in the video.


Jump to Chapters

Chapter 1: Discovering Game Theory 
Chapter 2: Research for a Ph.D. in Game Theory
Chapter 3: Degeneracy and the Simplex Method
Chapter 4: Al Tucker and Princeton
Chapter 5: The RAND Corporation
Chapter 6:  Linear Programming on Computers at RAND
Chapter 7:   The Frank-Wolfe Method for Nonlinear Programming
Chapter 8:   The Dantzig-Wolfe Decomposition Algorithm
Chapter 9:  Al Tucker and George Dantzig
Chapter 10:  Looking Back and Looking Forward

Jump to Chapters

Chapter 1: Discovering Game Theory
Chapter 2: Research for a Ph.D. in Game Theory
Chapter 3: Degeneracy and the Simplex Method
Chapter 4: Al Tucker and Princeton
Chapter 5: The RAND Corporation
Chapter 6: Linear Programming on Computers at RAND
Chapter 7: The Frank-Wolfe Method for Nonlinear Programming
Chapter 8: The Dantzig-Wolfe Decomposition Algorithm
Chapter 9: Al Tucker and George Dantzig
Chapter 10: Looking Back and Looking Forward

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 1978-80

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): 183-195.

Frank M. & Wolfe P. (1956) An algorithm for quadratic programming. Naval research logistics quarterly, 3(1‐2): 95-110.

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): 382-398.

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

Wolfe P. (1969) Convergence conditions for ascent methods. SIAM review, 11 (2): 226-235.

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

Crowder H. P., Held M., & Wolfe P. (1974) Validation of subgradient optimization. Mathematical Programming, 6 (1): 62-88.

Wolfe P. (1974) Note on a method of conjugate subgradients for minimizing nondifferentiable functions. Mathematical Programming, 7 (1): 380-383.

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: North-Holland.

Mathematical Programming Society: A History