Mathematical optimization has experienced tremendous growth in the last 20 years, and today, fundamental advances continue to occur at a furious pace. Spectacular progress has been made in our understanding of convex optimization problems and, in particular, of convex cone programming whose rich geometric theory and expressive power makes it suitable for a wide spectrum of important optimization problems arising in engineering and applied science. We have also learned how to approximate combinatorially hard optimization problems by simpler convex problems, which are tractable and provide solutions guaranteed to be close to the original optimal solution. In a different direction, robust optimization offers new techniques for handling data uncertainty by computing solutions that have a guaranteed regime of stability with respect to parameter perturbations, and prevents solutions to be too sensitive to noise or model errors. On the numerical side, recent remarkable advances in algorithms have made possible solving optimization problems involving tens of thousands of variables and/or constraints—even tens of millions in some instances—in reasonable time. These and other fundamental developments, along with progress in high-quality software, have expanded the scale and complexity of optimization problems that can be addressed in practice, and are leading to a wider adoption of optimization techniques throughout many fields in science and engineering.
The proposed long program will be centered on the development and application of these modern trends in optimization. It will bring together researchers from mathematics, computer science, operations research, engineering, and other fields, who have a common interest in optimization. Centered around five workshops, the goal is to develop and exchange ideas about modern optimization which can be influenced by, and influence in turn, progress in engineering and science.
Emmanuel Candes (Stanford University)
Masakazu Kojima (Tokyo Institute of Technology)
Monique Laurent (CWI, Amsterdam, and U. Tilburg)
Arkadi Nemirovski (Georgia Institute of Technology)
Yurii Nesterov (Université Catholique de Louvain)
Bernd Sturmfels (University of California, Berkeley (UC Berkeley))
Michael Todd (Cornell University)
Lieven Vandenberghe (University of California, Los Angeles (UCLA))