Mathematical Optimization is experiencing substantial advances. There have been remarkable developments in the underlying methods, for example, the emergence of interior methods for both linear and nonlinear optimization problems, the rediscovery of cuts as an effective tool for solving general integer programs, as well as for structured problems, and the emergence of new disciplines such as positive semidefinite programming which attack a broad variety of discrete and continuous problems. The problems being studied are much larger than before and the computing platforms are orders of magnitude more powerful. We believe that the 2002-2003 academic year will be an excellent time for the consolidation and advancement in this field that would be made possible by the focus of an IMA Special year. In addition, the next SIAM meeting on Optimization is scheduled for 2002, which should have a significant amount of synergy with an IMA Special Year on Optimization.
We propose to break the year into three semesters, each focusing on a different topic. The first will focus on the rapidly evolving area of supply chain, transportation and logistics optimization, as well as advances in integer programming. These are some of the fields placing increasingly large demands on the mathematical methods, as well as driving a focus on stochastic optimization and the notion of robustness.
The second semester will focus on advances in the underlying methods dealing with both nonlinear and linear optimization. Specific focus areas will probably include semidefinite programming, computational differentiation and nonconvex optimization.
The third will deal with the connections between optimization and information technology, an area that is proving to be increasingly important, and which would substantially benefit from a period of focus. This includes areas of discrete mathematics as well as areas such as network design and optimization.
We plan to hold a one-week introductory workshop at the beginning of the year, for the particular benefit of the optimization year postdocs. This will provide an overview of the state of the art in the underlying mathematical disciplines, and should provide a basis for much of the years activities. In addition, we will hold shorter tutorial workshops as needed during the three semesters.