CAREER: Towards an Analytical Perspective for Continuous Optimization Methods

Carnegie Mellon University, Pittsburgh PA

Investigators

Abstract

The central theme of this research plan is to formally study numerical issues concerning algorithms for continuous optimization. A primary goal is to address central topics in numerical analysis - such as perturbation theory, conditioning, and sparsity - in the continuous optimization context. A second objective is to gain further insight into interior point methods for convex programming. Special attention will be paid to numerical aspects such as the solution of the linear equations arising at each main iteration and the effects of limited precision in arithmetic computations. Properties of the central path and local convergence results will be studied. Applications of the analytical perspective for convex optimization in probability and discrete optimization will be explored. The educational plan involves activities both at the master and doctoral levels. At the master level, further development of courses in quantitative methods and applications of operations research will be pursued. Special emphasis will be placed on the role of mathematical models in a variety of industrial applications. At the doctoral level, exposure to interior point methods, semidefinite programming, and real model computation will be provided through the graduate nonlinear programming course, seminars, and reading courses.