In Memoriam: Philip Starr Wolfe (1927–2016)

By Harlan Crowder

Philip Wolfe

Photo credit: Michael Johnson

Philip Wolfe, one of the founding fathers of mathematical programming (MP), passed away on Dec. 29, 2016. Dr. Wolfe was a tireless researcher, teacher and avid promoter of the science and practice of MP. He was 89.

Dr. Wolfe was born in San Francisco in 1927. He received his Ph.D. from the University of California, Berkeley in 1954. His professional career carried him to the Pentagon, the mathematics department at Princeton University, the RAND Corporation in Santa Monica, Calif., and the Mathematical Sciences Department at IBM Research in Yorktown Heights, N.Y.

In 1951, while still a graduate student, Dr. Wolfe spent a summer internship working on the Air Force’s Project SCOOP at the Pentagon with George Dantzig. His most important accomplishment that summer was a suggestion for enabling Dantzig’s newly developed simplex method for linear programming (LP) to avoid a trap that could prevent the procedure from converging to optimality. Dr. Wolfe’s idea for avoiding cycling of LP solutions was included in a subsequent paper by Dantzig, Alex Orden and Dr. Wolfe.

Dr. Wolfe studied for his Ph.D. under the guidance of Edward Barankin at the University of California, Berkeley. He had become enamored with optimization during his stint at the Pentagon, but the new field of game theory, as presented by Von Neumann and Morgenstern in their landmark 1944 book “Theory of Games and Economic Behavior,” equally intrigued him. Unable to decide which of the two routes to follow, Dr. Wolfe did the logical thing and picked both; his two-part thesis, presented in 1954, was entitled “I. Games of infinite length. II. A non-degenerate formulation and simplex solution of linear programming problems.”

After receiving his Ph.D., Dr. Wolfe was lured to Princeton University by the opportunity to work with Albert Tucker and the stream of luminary visitors to the mathematics department, including George Dantzig, David Gale, Harold Kuhn, Theodore Motzkin and John von Neumann. One of his most significant accomplishments at Princeton was his collaboration with Marguerite Frank to study nonlinear optimization under linear constraints, resulting in the notable Frank-Wolfe procedure for quadratic programming.

The completed manuscript describing the Frank-Wolfe procedure, “An algorithm for quadratic programming,” was presented to the Naval Research Logistics Quarterly for publication. Coincidently, Harry Markowitz had also submitted a paper to the journal with a similar theme: “The optimization of a quadratic function subject to linear constraints.” The astute managing editor of the journal, Alan Hoffman, sent each the other’s paper for review. Both papers were favorably reviewed and were published in the same issue in 1956.

In 1957, Dr. Wolfe was drawn back West to join the RAND Corporation. The group there, including Dantzig, Ray Fulkerson and Lloyd Shapley, was developing practical computational methods for solving MP problems. In what was Dr. Wolfe’s best known work, he and Dantzig teamed up to develop the Dantzig-Wolfe decomposition method for linear programming. Their observations and ingenuity allowed the computational solution of a previously intractable class of problems.

By the mid-1960s, Ralph Gomory was director of the Mathematical Sciences Department (MSD) at IBM Research. MSD had several members who had made notable contributions to optimization and operations research (O.R.), including Gomory, Hoffman, Paul Gilmore, T. C. Hu and Richard Karp. In 1966, Gomory, who had known Dr. Wolfe since they had collaborated at RAND, invited Phil to join MSD. Once again Dr. Wolfe journeyed east and joined IBM Research where he would stay until his retirement.

Dr. Wolfe was soon asked to form a group within the department that would focus on optimization and O.R. He enlisted MSD members including Ellis Johnson, Earl Barnes and Harlan Crowder. He also fostered collaboration and recruited ex officio members from inside and outside IBM, including Manfred Padberg, Michael Held, Kurt Spielberg and Peter Norden. This effort by Dr. Wolfe and his colleagues ultimately helped establish IBM Research as a major center of excellence in the theory and practical application of mathematical optimization.

At IBM, Dr. Wolfe’s research interests dealt with various aspects of nonlinear optimization, including globally convergent methods for unconstrained optimization and nondifferentiable optimization.

Dr. Wolfe also applied his leadership and collaboration talents to establishing a professional community for the continuing development of MP. He was active in the Association for Computing Machinery and its Special Interest Group in Mathematical Programming. In 1970, he collaborated with Michel Balinski to establish the journal Mathematical Programming. The next year, he was one of the principal founders of the Mathematical Programming Society (MPS); he served as MPS chairman from 1978 to 1980.

One of Dr. Wolfe’s favorite creations was the Friends of Optimization (FoOp), an informal organization in the New York metropolitan area devoted to discussions and presentations on optimization and O.R. FoOp’s lively meetings were held at various venues and were a valuable opportunity for collaboration among participants from academia, government and industry.

When the Russian mathematician L.G. Khachiyan’s polynomial-time ellipsoid algorithm for LP was announced in 1979, it was misconstrued in the popular press. A New York Times reporter wrote, “Soviet mathematician is obscure no more” and “the mystery author of a new mathematical theorem has rocked the world of computer analysis.” Dr. Wolfe was soon receiving invitations from around the world to put in perspective the theoretical value of Khachiyan’s work and its modest contribution for solving real-world LP problems.

Dr. Wolfe was a Fellow of the American Association for the Advancement of Science, the Econometric Society and the Institute for Operations Research and the Management Sciences (INFORMS). In 1992, he received the John von Neumann Theory Prize, jointly with his friend and colleague Alan Hoffman, from the Operations Research Society of America, a forerunner of INFORMS. He received a Distinguished Service Award and a Founders Award from the MPS in 2000.

In academic teaching pursuits, Dr. Wolfe served as an adjunct professor for the Industrial Engineering and Operations Research Department at Columbia University, and for the mathematics departments at The City University of New York and the New York (Brooklyn) Polytechnic Institute.

Dr. Wolfe is survived by his wife Hallie Flanagan Wolfe, daughter Sarah of Whitehorse, Canada, and grandchildren Duncan and Sidney.


  1. Irv Lustig, INFORMS History and Traditions Interviews, INFORMS, 2001.
  2. Alan J. Hoffman, in “Profiles in Operations Research,” Springer, 2011.