Harold W. Kuhn

Brief Biography

An important figure in mathematical programming and game theory, Harold Kuhn's earned a bachelor's degree from California Institute of Technology (1947). His undergraduate progress at Caltech had been interrupted during World War II when he was drafted into the U. S. Army. When he passed a qualifying examination in linguistic proficiency, he was transferred to the Army Specialized Training Program in Japanese at Yale University, where he studied to become an interpreter for war crime trials. However a knee operation left him unable to go to Japan, he was, discharged and he returned to Caltech to complete his BS in mathematics. This was followed by a master's degree (1948) and P.h.D (1950) in mathematics from Princeton University, where he would eventually return, after a stint at Bryn Mawr, to teach and conduct research for 37 years. He retired from Princeton in 1995.

Kuhn received his doctorate at a pivotal time in the mathematical foundations of OR, particularly in the Princeton environment. Inspired by George Dantzig's U. S. Air Force-sponsored research that led to the development of the simplex method in linear programming, Princeton Professor Albert Tucker obtained funding from the Office of Naval Research (ONR) to launch a research project that would further explore duality relationships in mathematical programming. He convinced Kuhn and David Gale to join the team, which led to Kuhn's first contributions to OR theory at Princeton.

Originally focused in his doctoral thesis on topology and algebra, Kuhn's involvement in the ONR grant shifted his interests to optimization and decision theory, as the group studied von Neumann and Morgenstern's Theory of Games and Economic Behavior (1944) and other seminal work . Questions regarding the relationship between linear programming and the theory of electrical networks developed into an investigation by Tucker and Kuhn of duality in quadratic programming, and eventually in general nonlinear programming. At a RAND conference in 1950 they showed conditions for the relationship between primal and dual nonlinear programming (NLP) problems, eventually named the Karush-Kuhn-Tucker (KKT) conditions.

Gale, Kuhn, and Tucker also extended duality results to the vector maximization problem, which involves the simultaneous maximization of multiple objectives subject to linear or nonlinear constraints, and applied them to activity analysis and economic competitive equilibrium problems. .They eventually received the John von Neumann Theory Prize in 1980 for their work.

In addition to his work on duality in NLP, Kuhn is also known for the development.of the Hungarian Method, an algorithm for the problem of assigning of workers to tasks, which he published in the Naval Research Logistics Quarterly in 1955. The Hungarian Method was later shown to be the first algorithm of polynomial complexity for a large class of linear programs. In 2005, the Naval Research Logistics journal recognized Kuhn's 1955 publication as the best paper in the 50 years since its founding.

 Kuhn is also known in relation to fellow graduate student John Nash, who suffered from mental difficulties chronicled in the book and film "A Beautiful Mind." Kuhn edited Nash's papers and was instrumental in the award to Nash of the 1994 Prize in Economic Sciences in Memory of Alfred Nobel. This Nobel Prize is a testament to Kuhn's abiding interest in bringing mathematical approaches to economics.

Beyond his professorship, Kuhn served as Scientific Director and Board Member for Mathematica, Inc. from 1961 to 1983. He was also administratively involved at Princeton as secretary of the Faculty Advisory Committee to the President and a member of the Committee on the Governance of the University.

Dr. Kuhn's undergraduate and graduate teaching career included courses in price theory, managerial economics, micro-economics, mathematical economics, trade theory, game theory, and linear and nonlinear programming. His mathematical programming course consistently made the overall "Top Ten" list at Princeton, a distinction which led undergraduates such as John Birge and David Shmoys to take the course that established their career direction.

 Kuhn's honors and awards include: recipient of the Guggenheim Fellowship; elected member of the American Academy of Arts and Science; elected fellow of the Econometric Society, 1961; and elected fellow of the Society for Industrial and Applied Mathematics (SIAM), 2009. His leadership positions include: member of the first council of SIAM and its third president; Executive Secretary, Division of Mathematics, National Research Council, 1957-60; and council member of the American Association of University Professors, 1959-62. Kuhn was also elected an Honorary Member of the Hungarian Operational Research Society in 1992 and received an Honorary Doctorate in Economics from the University of Bergamo, Italy in 2001.

Professor Harold Kuhn died July 2, 2014.

Other Biographies

• Gass, Saul I. and Guillermo Owen, Harold W. Kuhn, chapter 29 in Assad, Arjang and Saul I. Gass, Profiles in Operations Research, Springer, 2011. 
• Harold W. Kuhn, in IFORS' Operational Research Hall of Fame, International Transactions in Operations Research 11 (2004) 715–718