Early life and family Cottle was born in
Chicago on 29 June 1934 to Charles and Rachel Cottle. He started his elementary education in the neighboring village of
Oak Park, Illinois, and graduated from
Oak Park-River Forest High School. After that, admitted to Harvard, Cottle began by studying government (political science) and taking premedical courses. After the first semester, he changed his major to
mathematics in which he earned his
bachelor's (cum laude) and
master's degrees. Around 1958, he became interested in teaching secondary-level mathematics. He joined the Mathematics Department at the
Middlesex School in
Concord, Massachusetts, where he spent two years. Midway through the latter period, he married his wife, Suzanne.
Career Source: While teaching at Middlesex School, he applied and was admitted to the
PhD program in mathematics at the University of California at Berkeley, with the intention of focusing on geometry. Meanwhile, he also received an offer from the
Radiation Laboratory at Berkeley as a part-time computer programmer. Through that work, some of which involved linear and quadratic programming, he became aware of the work of
George Dantzig and
Philip Wolfe. Soon thereafter he became a member of Dantzig's team at UC Berkeley Operations Research Center (ORC). There he had the opportunity to investigate quadratic and convex programming. This developed into his
doctoral dissertation under the guidance of Dantzig and Edmund Eisenberg. Cottle's first research contribution, "Symmetric Dual Quadratic Programs," was published in 1963. This was soon generalized in the joint paper "Symmetric Dual Nonlinear Programs," co-authored with Dantzig and Eisenberg. This led to the consideration of what is called a "composite problem," the first-order optimality conditions for symmetric dual programs. This in turn, was named "the fundamental problem" and still later (in a more general context) "the complementarity problem." A special case of this, called "the linear complementarity problem", is a major part of Cottle's research output. Also in 1963, he was a summer consultant at the
RAND Corporation working under the supervision of Philip Wolfe. This resulted in the RAND Memo, RM-3858-PR, "A Theorem of Fritz John in Mathematical Programming." In 1964, upon completion of his doctorate at Berkeley, he worked for
Bell Telephone Laboratories in
Holmdel, New Jersey. In 1965, he was invited to visit Stanford's OR Program, and in 1966, he became an Acting Assistant Professor of Industrial Engineering at Stanford. The next year he became an assistant professor in Stanford's new Department of Operations Research. He became an associate professor in 1969 and full professor in 1973. He chaired the department from 1990 to 1996. During 39 years on the active faculty at Stanford he had over 30 leadership roles in national and international conferences. He served on the editorial board of eight scholarly journals, and was editor-in-chief of the journal
Mathematical Programming. He served as the associate chair of the Engineering-Economic Systems & Operations Research Department (EES & OR) after the merger of the two departments. In 2000, EES & OR merged again, this time with the Industrial Engineering & Engineering Management Department to form Management Science and Engineering (MS&E). During his sabbatical year at Harvard and
MIT (1970-1971), he wrote “Manifestations of the Schur Complement’’, one of his most cited papers. In 1974, he started working on “The Linear Complementarity Problem,” one his most noted publications. In the mid 1980s, two of his former students, Jong-Shi Pang and Richard E. Stone, joined him as co-authors of this book which was published in 1992. “The Linear Complementarity Problem” won the
Frederick W. Lanchester Prize of the Institute for Operations Research and the Management Sciences (INFORMS) in 1994. “The Linear Complementarity Problem” was republished by the Society for Industrial and Applied Mathematics in the series “Classics in Applied Mathematics series” in 2009. During 1978–1979, he spent a sabbatical year at the
University of Bonn and the University of Cologne. There he wrote the paper “Observations on a Class of Nasty Linear Complementarity Problems’’ which relates the celebrated Klee-Minty result on the exponential time behavior of the simplex method of linear programming with the same sort of behavior in Lemke's algorithm for the LCP and hamiltonian paths on the n-cube with the binary Gray code representation of the integers from 0 to 2^n - 1. Also during this time he solved the problem of minimally triangulating the n-cube for n = 4 and worked with Mark Broadie to solve a restricted case for n = 5. In 2006 he was appointed a fellow of INFORMS and in 2018 received the Saul I. Gass Expository Writing Award. == Contributions ==