Program Summary
The Lagrange program seeks to develop new mathematical approaches to optimization problems in uncertain, dynamic, multiscale, and high-dimensional settings. By bridging methodologies developed for both discrete and continuous optimizations, Lagrange aims to enable solutions for complex, realistic problems that involve dynamic environments, rapidly changing requirements, and increasing or decreasing amounts of information.
In particular, Lagrange will address the fact that many applications of interest today are posed as non-convex optimization problems and thus remain intractable despite significant recent theoretical and algorithmic progress in convex optimization. Lagrange seeks methodologies beyond current convex relaxation methods to advance scalability of algorithms; data-driven approaches that explore proper sampling of data sets; and computationally tractable methods of approximating distributions.
Expected outcomes of the program include: 1) new mathematical frameworks and solution methods for large-scale optimization of complex systems, and 2) algorithms that could be implemented on computing platforms that would use parallelizability and scalability.