The 2017 Farkas Prize of the INFORMS Optimization Society is awarded to Kim-Chuan Toh, Provost Chair, Department of Mathematics, National University of Singapore, for his fundamental contributions to the theory, practice, and application of convex optimization, especially semidefinite programming and conic programming.
Toh is among the world's leading figures in semidefinite programming, an important part of optimization since the early 1990s. His research collaboration with Michael Todd and Reha Tutuncu on interior-point methods for semidefinite programming produced SDPT3, a Matlab software package including parts written in C and integrated via MEX files. SDPT3 incorporated the then-latest theoretical developments in semidefinite programming and large-scale linear solvers, and provided a "proof of concept" that semidefinite programming models were mathematically and computationally appealing. SDPT3 remains in wide use today, having been repeatedly updated to incorporate new algorithmic and programming features.
Toh's contributions (with a variety of coauthors) have also advanced the state of the art in convex optimization in two broad directions. First, new methods have been devised for several specific problem classes in data science, including matrix completion, image restoration, covariance selection, feature extraction, and nuclear-norm minimization. Second, for general convex optimization problems, Toh's work has led to a selection of first-order methods: proximal point, alternating direction method of multipliers, and augmented Lagrangian. All of these are associated with novel preconditioners for very large linear systems.
Each of Toh's contributions is an impressive mixture of new theoretical insights, numerically sound algorithmic strategies, and efficient implementation.
Margaret Wright (chair), Patrick Jaillet, Zhi-Quan (Tom) Luo, Pascal Van Hentenryck.