Tamás Terlaky (left), Celso Ribeiro, Clóvis Gonzaga, and Sanjay Mehrotra.
The 2014 recipients of the INFORMS Optimization Society Khachiyan Prize, for their remarkable life-time achievements in the area of optimization, are Clóvis C. Gonzaga, Professor of Mathematics at the Federal University of Santa Catarina, Florianópolis, Brazil, and Dimitri Bertsekas, McAfee Professor of Engineering at the Massachusetts Institute of Technology.
Clóvis C. Gonzaga has been working on continuous optimization for the last 40 years. He was one of the founders of the Systems and Computation Dept. at the Federal University of Rio de Janeiro, where he was the first person in Brazil to teach non-linear programming. He worked simultaneously on graph search methods, continuous optimization and on optimal power systems. He was responsible for the software used in Brazil for many years to plan the expansion of the Brazilian power transmission system.
During his remarkable career, Clóvis Gonzaga has grown to be one of the world's foremost experts in the area of continuous optimization, with main interest in the fundamental problems of Interior Point methods (IPMs). Since the mid 80's, as one of the leading developer of IPMs, Gonzaga is among the most recognized optimization researchers. His 1989 seminal paper, "An algorithm for solving linear programming problems in O(n^3L) operations," contains the analysis of a path-following method that till today yields the best complexity bound for solving linear optimization problems. His 1992 SIAM Review paper "Path-following methods for linear programming" is among the most influential papers that inspired and motivated many researchers.
While Gonzaga has remained to play a key role in the developments of IPMs, recently he also worked on augmented Lagrangean methods, on filter methods for constrained non-linear optimization, and on fast steepest descent methods. He has recently developed steepest descent algorithms for the minimization of convex quadratic functions with the same performance bound as Krylov space methods.
Clóvis Gonzaga has been active in teaching and spreading the interest for continuous optimization worldwide. He is a SIAM fellow, a member of the Brazilian Academy of Sciences and of the World Academy of Sciences, and received the Great Cross of the Brazilian Order of Scientific Merit. He was a plenary or semi-plenary speaker in several prime conferences, such as ISMP (twice), SIOPT, IFIP, IFORS, ICIAM.
Dimitri Bertsekas has made fundamental contributions to multiple areas of optimization including theory, computation, and applications. He has also contributed to optimization knowledge broadly through the clarity of exposition in his many books on optimization topics and the accomplishments of his students who have in turn made significant advances in the field.
Professor Bertsekas's theoretical contributions include his resolving the question of conditions for a consistent recursive form for dynamic programming with uncountable state spaces through the introduction of universally measurable spaces. He also helped establish the theoretical foundation for Lagrangian methods in nonlinear programming with general convergence results, duality theory, and procedures and bounds for nonconvex formulations. His more recent theoretical work includes a comprehensive view of the basic properties underlying dynamic programming and a geometric interpretation of duality and general optimality conditions with algorithmic implications.
In algorithmic development, Professor Bertsekas was a pioneer in network optimization through his development of the classes of auction and relaxation algorithms. These methods led not only to some of the most efficient algorithms in practice but to many new theoretical discoveries in the field. In addition, Professor Bertsekas's work includes the exposition of the generalized alternate direction method that has recently become a foundation for work in machine learning and statistical inference in large data sets.
In addition to his many specific research contributions, Professor Bertsekas's books have exposed many researchers, practitioners, and students in a wide range of fields to the principles of optimization. His work has had a profound influence on numerous domains such as signal processing, communications, power systems, transportation, logistics, and economics. His many students have expanded his work even more broadly, adding to his continued and lasting impact on the field.
The two winners of the Khachiyan prize were invited to give a short talk (about 15 minutes) at the INFORMS Annual Meeting. Below are links to the recordings of these talks.
Tamás Terlaky (chair), Daniel Bienstock, Immanuel Bomze, John Birge