Richard W. Cottle

June 29, 1934

Brief Biography

Cottle Fellow Portrait

Richard W. Cottle is a Frederick W. Lanchester Prize recipient (1994), as well as a recipient in 2018 of the INFORMS Saul Gass  Expository Writing award for his collection of articles on the history of ORMS. See the references listed below, such as the curious story of William Karush and the (re)discovery of the (K)KT conditions.  Cottle is best known for his contributions to mathematical programming. Cottle received his first two degrees at Harvard University before continuing his education at the University of California, Berkeley. At Cal Berkeley, he studied under and developed a close working relationship with George B. Dantzig, the father of linear programming (Cottle and Dantzig went on to publish many articles together). In 1964, he wrote "Nonlinear Programs with Positively Bounded Jacobians" (his dissertation that was later published in the SIAM Journal on Applied Mathematics), and received a PhD in mathematics. 

Cottle’s first position out of graduate school was with AT&T Bell Laboratories in Holmdel, New Jersey. For two years he was on the lab's technical staff. Cottle took leave from Bell Labs during the 1966-1967 academic year in response to an invitation to teach in the Operations Research Program at Stanford.  While there, he accepted a position in the newly formed Stanford Operations Research Department. Cottle became full professor in 1973 and served as department chair from 1990 to 1996. In the late seventies, he conducted research at the universities of Bonn and Cologne as a recipient of the Alexander von Humboldt Foundation’s U.S. Senior Scientist award. In 2002, he spent a term as the Arthur Andersen Distinguished Visitor at the Judge Institute of Management Studies at Cambridge in the United Kingdom.

At Stanford, Cottle developed collaborative relationships with many of his fellow faculty members. In 1992, Cottle co-wrote The Linear Complementarity Problem with Richard Stone, then at Northwest Airlines (now at Delta Airlines) and Jong-Shi Pang, then  at Johns Hopkins University (now at the University of Southern California). In 1994, the book and its authors received one of two Lanchester Prizes, which are awarded to the most significant contribution to operations research and the management sciences published in English in the prior three years (the other went to Professor Edward Kaplan for his papers on AIDS modelling). The publication by Cottle, Pang amd Stone was celebrated as a “unique and comprehensive treatment of all major aspects of the linear complementarity problem”. As brought out in the book,  complementarity problems  are inherent in the theory of mathematical optimization, and have applications in computer  science, economics, engineering, finance, game theory, and mathematics. Nearly twenty-five years later, The Linear Complementarity Problem remains an important part of complementarity research and education, and in 2009 it was republished in the SIAM Classics in Applied Mathematics series.

In addition to linear complementarity, Cottle has researched and published on a variety of mathematical programming topics, including quadratic and nonlinear optimization. In 2006, he was recognized for his outstanding contributions to operations research and was elected a Fellow of the Institute for Operations Research and the Management Sciences. Though he is now retired, Cottle remains actively involved in the Stanford community. In the early 1990s, he began a research project on the historical background of the more than one-hundred and thirty street names on the university's campus. His work came together in the 2005 field guide, Stanford Street Names: A Pocket Guide, which was republished in revised and updated form in 2014.  A more recent publication, with Mukund N. Thapa, is the textbook Linear and Nonlinear Optimization.

Other Biographies

Richard W. Cottle (2015), Stanford Historical Society Oral History Program Interviews (SC0932). Department of Special Collections & University Archives, Stanford University Libraries, Stanford, Calif. (link with audio and downloadable transcript including a biography and cv)


Harvard University, AB 1957

Harvard University, AM 1958

University of California Berkeley, PhD 1964 (Mathematics Genealogy


Academic Affiliations
Non-Academic Affiliations

Key Interests in OR/MS


Oral Histories

Richard W. Cottle (2015), Stanford Historical Society Oral History Program Interviews (SC0932). Department of Special Collections & University Archives, Stanford University Libraries, Stanford, Calif. (link with audio and downloadable transcript)

Awards and Honors

Frederick W. Lanchester Prize 1994

Institute for Operations Research and the Management Sciences Fellow 2006

INFORMS Saul Gass Expository Writing Award 2018

Selected Publications

Dantzig G. B. & Cottle R. W. (1963) Positive (semi-) Definite Matrices and Mathematical Programming. University of California Berkeley Operations Research Center: Berkeley, CA.

Cottle R. W. (1966)  Nonlinear programs with positively bounded Jacobians. SIAM Journal on Applied Mathematics, 14(1): 147-158.

Cottle R. W. & Dantzig G. B. (1968) Complementary pivot theory of mathematical programming. Linear Algebra and its Applications, 1: 103-125.

Cottle R. W. & Dantzig G. B. (1970) A generalization of the linear complementarity problem. Journal of Combinatorial Theory, 8(1): 79-90.

Cottle R. W. & Veinott Jr A. F. (1972) Polyhedral sets having a least element. Mathematical Programming, 3(1): 238-249.

Cottle R. W., Giannessi F. & Lions J.L.  eds. (1980) Variational Inequalities and Complementary Problems: Theory and Applications. John Wiley & Sons: New York. 

Cottle R. W., Pang J. S., & Venkateswaran V. (1989) Sufficient matrices and the linear complementarity problem. Linear Algebra and Its Applications, 114: 231-249.

Cottle R. W., Pang J. S., & Stone R. (1992) The Linear Complementarity Problem. Academic Press: Boston.  Republished by SIAM: Philadelphia, 2009.

Arrow K. J., Cottle R. W., Eaves B. C., & Olkin I., eds. (1996) Education in a Research University. Stanford University Press: Stanford, CA.

Cottle R. W. (2003) The Basic George B. Dantzig. Stanford University Press: Stanford, CA.

Cottle R. W. (2005) George B. Dantzig: Operations Research Icon. Operations Research, 53(6): 892-898.

Cottle, R. W. (2012)  William Karush and the KKT Theorem. In Grötschel, M. ed. Documenta MathematicaExtra Volume "Optimization Stories" 255-269. (link)

Cottle R. W. & Thapa, M. N. (2017) Linear and Nonlinear Optimization.  Springer: New York.

Cottle R. W. (2017) 'Pre-Historic’ Linear Programming and the Figure of the Earth. Journal of Optimization Theory and Applications 175: 321-327.