Carlton E. Lemke

October 11, 1920 – April 12, 2004

Brief Biography

Carlton Edward Lemke, born in Buffalo, New York, was a leading figure in mathematical programming and game theory. Lemke grew up in a Polish neighborhood and picked up boxing at an early age. He served in the 82nd Airborne Paratrooper Division of United States Army’ and saw action in the Allied Invasion of Sicily. Lemke returned to New York after World War II to study at the University of Buffalo. He went on to the Carnegie Institute of Technology (Carnegie-Mellon University) and received his PhD under the supervision of Abraham Charnes. As a graduate student, Lemke mentored and advised undergraduates interested in operations research.

Lemke spent his first year after graduate school as a research associate at General Electric before taking up an operations analysis position at the Radio Corporation of America. He returned to his native state of New York to accept a professorship at Rennselaer Polytechnic Institute in Troy. Lemke remained at Rensselaer for the rest of his career, retiring from teaching in 1988.

Lemke made numerous significant contributions to mathematics and operations research, largely dealing with mathematical programming and the theory of games. By 1954, he had built upon the work of George B. Dantzig and invented the Dual Simplex Method for linear programming. In 1962, he devised a method of solution for quadratic programs, which require minimizing a strictly convex quadratic functional of several variables constrained by a system of liner inequalities.

Leading into the 1960s, game theory had reached somewhat of a standstill. While future Nobel Prize-winning economist John Nash had conceived the idea of non-cooperative equilibrium in multi-person games, it seemed as if the nonlinearity of many problems would prevent the actual numerical solution of any but the simplest of games. Lemke, along with J. T. Howson, Jr, devised an ingenious algorithm for the bimatrix case (i.e. finite, non-zero sum two person games). Lemke took the lead in exploiting the many ramifications and applications of this procedure. For this outstanding contribution he, along with Nash, received the John von Neumann Theory Prize from the Operations Research Society of America.

Lemke was elected into the inaugural class of Fellows of the Institute for Operations Research and the Management Sciences in 2002. Even late in his life, he was known to have jogged on a nearly daily basis, counting every single one of his steps. Upon retirement, he relocated to Tucson, Arizona where he remained until his death in 2004. 

Other Biographies

Wikipedia Entry for Carlton E. Lemke

Wikipedia Entry (Deutsch) for Carlton E. Lemke


University of Buffalo, BS 1949

Carnegie Instiute of Technology, MS 1951

Carnegie Institute of Technology, PhD 1953 (Mathematics Genealogy


Academic Affiliations
Non-Academic Affiliations

Key Interests in OR/MS



Rensselaer Polytechnic Institute Faculty Senate. 2004/2005 Memorials: Carlton E. Lemke. Accessed March 21, 2015. (link

Awards and Honors

John von Neumann Theory Prize 1978

Institute for Operations Research and the Management Sciences Fellow 2002

Selected Publications

Charnes A. & Lemke C. E. (1954) Computational Theory of Linear Programming. 1. The Bounded Variables Problem. Carnegie Institute of Technology Graduate School of Industrial Administration: Pittsburgh, PA.

Lemke C. E. (1954) The Dual Method of Solving the Linear Programming Problem. Naval Research Logistic Quarterly, 1(1): 36-47.

Lemke C. E. (1962) A Method of Solution for Quadratic Programs. Management Science, 8(4): 442-453.

Howson Jr J. T. & Lemke C. E. (1964) Equilibrium points of bimatrix games.Journal of the Society for Industrial & Applied Mathematics, 12(2): 413-423.

Lemke C. E. (1965) Bimatrix equilibrium points and mathematical programming. Management Science, 11(7): 681-689.

Lemke C. E. (1967) On complementary pivot theory. Department of Mathematics, Rensselaer Polytechnic Institute: Troy, NY.

Cottle R. W., Habetler G. J., & Lemke C. E. (1970) On classes of copositive matrices. Linear Algebra and Its Applications, 3(3): 295-310.

Cottle R. W. & Lemke C. E. (1976) SIAM-AMS Proceedings Volume IX: Nonlinear Programming. The American Mathematical Society: New York. 

Additional Resources

A Dinner Talk Remembering C. E. Lemke. Complexity of Games, Polyhedra and Lattice Points. May 17-19, 2006. FIM, ETH Zurich Switzerland. (link)