Robinson Wins Prize in Math Programming
Industrial and Systems Engineering professor Stephen M. Robinson has won a top international award for mathematical programmers. Robinson received the George B. Dantzig Prize during a ceremony July 18 at Stanford University. He is one of two 1997 recipients, along with Roger Fletcher of the University of Dundee, Scotland. The leading professional associations in the field, the Mathematical Programming Society and the Society for Industrial and Applied Mathematics award the Dantzig Prize only once every three years. The prize, which includes a $2,000 cash award, is given for original work that makes an outstanding new contribution to the field.

Mathematical programming is the development of mathematical methods for making the best use of limited resources. It is frequently used to improve operations in realworld applications such as manufacturing or transportation. Robinson conducts both theoretical and applied research to develop better methods for quantitative economic planning, which falls into the broad category of operations research methods. Within that category, he has developed nonlinear and stochastic optimization methods.
Robinson is working both on developing the underlying theory of these methods and on finding better computational methods to solve problems. For example, in a series of four related papers. Robinson introduced a mathematical construction, the generalized equation, that can conveniently be used to model a wide variety of practical problems arising in economics, operations research, transportation, mechanics and other areas. The common feature of these problems is that they lead either to necessary optimality conditions for constrained optimization problems or to equilibrium formulations. People trying to analyze such problems had been blocked by the fact that the problems contain nonsmooth elements (or corners) arising from inequality constraints such as nonnegativity. Often the underlying functions in these problems are smooth, but this smoothness could not be exploited to analyze the problems because of the corners. Robinson showed how the equilibrium conditions for all such problems could be written in a unified way as 0 belongs to f(x) +T(x) where "f" is a smooth function containing all of the "nonlinearity" in the problem and T essentially collects all of the corners. For the usual kind of nonlinear equation T is identically zero, so this is a genuine extension of the classical idea of an equation. Robinson then showed that one could apply numerous techniques of analysis to the smooth component "f", just as in the case of ordinary nonlinear equations, while carrying the operator T along. The result was a quantum advance in the technology for analyzing, and the algorithms for solving, optimization and equilibrium problems. These methods are now a standard part of the subject's fundamental theory and are used by researchers worldwide.