aslewis (AT) orie.cornell.eduSchool of Operations Research and Industrial Engineering Personal Website
Optimization is the mathematical and computational study of how to minimize or maximize a function subject to constraints. Such problems are fundamental throughout pure and applied mathematics, and are an important modeling tool in many applications. Traditional calculus is often useless in interesting optimization problems, because the functions involved are nonsmooth.
I am particularly interested in "eigenvalue optimization". Many important concrete optimization models involve eigenvalues of symmetric and nonsymmetric matrices: engineering design is a particularly significant source. Concurrent with a growing interest in eigenvalue optimization, if differently motivated, "variational analysis" has developed over the last couple of decades into a mature theoretical tool for nonsmooth functions such as eigenvalues. I explore theory and algorithms at the interface between these two areas.