Richard W. Cottle (29 June 1934) is an American mathematician. He was a professor of Management Science and Engineering at Stanford University, starting as an Acting Assistant Professor of Industrial Engineering in 1966 and retiring in 2005. He is notable for his work on mathematical programming/optimization, “Nonlinear programs”, the proposal of the linear complementarity problem, and the general field of operations research.
Life and career
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
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."