Nick Sahinidis (left) and Tom Luo.
Tom Luo has made fundamental contributions to optimization theory and its applications that include many topical problems in signal processing and digital communication. His work on the complementarity and equilibrium problems, error bound analysis, extensions of Frank-Wolfe theorem to quadratic constraints, interior point methods for conic programming problems, and convex relaxation for NP-hard optimization has made a profound impact to the field. Together with Paul Tseng, he proved the convergence analysis of matrix splitting algorithms for linear complementarity problems and affine variational inequalities, analyzed the convergence of the affine scaling algorithm for linear programs, developed (with Jos Sturm and Shuzhong Zhang) a superlinearly convergent primal-dual interior point algorithm for semidefinite programming without the non-degeneracy assumption, and produced a constant lower bound for the approximate S-lemma and a constant approximation ratio for random least squares over binary variables. His book (jointly with Pang and Ralph) on Mathematical Programs with Equilibrium Constraints laid a strong theoretical foundation for the subject and has inspired many to work in this area of research. In communication, he developed a Second-Order Cone program for beam-forming that admits very efficient solution via modern interior point methods, and showed (with Shuzhong Zhang) zero-duality for a broad class of dynamic spectrum management problems for single-tone and multi-tone multi-user interference channels. His recent work on quartic programming opens a new chapter for this class of nonconvex optimization problems with significant practical applications.
For all his contributions, Tom Luo is eminently deserving of the 2010 Farkas Prize awarded by the Optimization Society within the Institute for Operations Research and Management Science.
Gerard Cornuejols, Jong-Shi Pang (chair), Kees Roos, Yinyu Ye