My research

Broadly speaking, my research focuses  on theory and implementation of high-performance optimization algorithms.
I am currently concentrating on several topics:

  • Fundamental methodologies for nonconvex optimization and integer programming.  We are studying techniques for provably tightening formulations of mixed-integer programs.  Here, 'provably' means that we seek guarantees (e.g. error bounds).  Thus, in an ideal setting an improved formulation is polynomially large and guarantees a 'small' approximation error.  Our primary technique in this context is the use of carefully selected combinatorial disjunctions.  Another focal area involves the use of eigenvalue techniques in order to tighten formulations for convex objective, nonconvex (but possibly noncombinatorial) optimization problems.  Problems of this type abound in engineering applications, where the convex objective is often a measure of "error" or "energy", while the underlying physics impose significant nonconvexities.  This work is funded by ONR.

  • Using optimization techniques for improving power grid operations.  Impending changes in power generation and distribution give rise to challenging and interesting opportunities for optimization, data science and economics. We are currently engaged in a number of research projects in this direction. This work is currently funded by the U.S. Department of Energy, DTRA, DARPA and ARPA-E.  Also see this announcement on our recently funded ARPA-E project.

  • CV and publication list (not quite up to date): here.