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.
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.