Robert has made important contributions to a broad spectrum of topics in optimization covering both theory and application.
At the early stage of the development of interior point methods, Robert made fundamental contributions to our understanding of these methods, such as the affine scaling method, for linear programming and their extension to convex and nonconvex optimization. In a long-term collaboration with Hande Benson and David Shanno, he has analyzed the efficacy of various filter methods, penalty methods, and merit functions for nonlinear optimization. In addition to contributing to the extensive research on worst-case performance, he has developed then state-of-the-art software to solve these problems. As is well-known, the efficiency of a linear programming algorithm is greatly influenced by the sparsity of the constraint matrix and he has introduced a number of creative techniques to find equivalent sparse representations of a given problem.
One of the first papers on the important area of robust optimization was written by Robert and his co-authors John Mulvey and Stavros Zenios.
Robert, working collaboratively with Hemlberg, Rendl, and Wolkowicz, developed one of the first primal-dual algorithms for semi-definite programming, which was one of the important open questions in the middle of the 1990s.
Robert has published a broad variety of applications of optimization. One such application is the design of a NASA space telescope that will be able to image Earth-like planets orbiting Sun-like stars. Building such a telescope requires solving a discrete approximation to an infinite-dimensional linear programming problem in which the integral of a continuous function is maximized subject to constraints on the Fourier transform of the function. Robert observed that the fast Fourier transform can be viewed as a matrix sparsification technique and that the same idea, called "Fast Fourier Optimization," can be applied to other problems.
Robert has written three books including a popular textbook on linear programming.
Robert is a Fellow of INFORMS, SIAM, and the AMS. He has also served INFORMS in various ways including as the Chair of the Optimization Society, Chair of the Computing Society, and as a member of the Subdivisions Council. He has also served as an associate editor for several journals including Operations Research, the INFORMS Journal on Computing, and Mathematical Programming.
Gerald Brown (chair), Bill Cook, Andrzej Ruszczyński, and Yinyu Ye.