Methodological research in optimization uses techniques of algebra, geometry, analysis and combinatorics to develop and analyze algorithms for fundamental optimization models having broad applicability. Such models are the means by which we can leverage general-purpose optimization software for applications in all areas. For very large scale applications, specially tailored algorithms are developed.
This area includes:
Integer Optimization: Integer variables are key for modeling logical decisions. Developing algorithms to handle large-scale models with integer variables is an important application-enabling topic. Research in this area makes strong use of geometry, algebra, and combinatorics.
Robust and Stochastic Optimization: Modeling uncertainty in a tractable manner to address applications involving uncertainty by linking data analytics with optimization. Scaling algorithms to handle large instances enables us to make better use of data for decision making. Research in this area makes strong use of geometry, algebra, and analysis.
Combinatorial Optimization and Approximation Algorithms: This area focuses on problems involving combinatorial choices (e.g., network design, facility location, scheduling), with the goal of developing fast and accurate algorithms. Research in this area makes strong use of combinatorics and algebra.
Continuous Optimization: At the heart of many decision problems in engineering and machine learning, and at the core of all kinds of optimization algorithms are continuous optimization problems. Fast, scalable algorithms in this domain have practical ramifications in many contexts.