My area of research is mathematical optimization. For the last couple years I’ve been focusing on convex relaxations for continuous nonconvex problems. The principle for obtaining these relaxations is to exploit a certain equivalence between optimization and certifying function nonnegativity. I have developing interests in applied algebraic geometry and second-order methods for constrained convex optimization.
Signomial and Polynomial Optimization via Relative Entropy and Partial Dualization
With Venkat Chandrasekaran and Adam Wierman. Currently available on arXiv. The mathematics described in this paper are implemented by the sageopt python package. I don’t have any recordings of talks on this topic, however I can offer a couple sets of slides (MPI MiS 2019, ICCOPT 2019).
Newton Polytopes and Relative Entropy Optimization.
With Venkat Chandrasekaran and Adam Wierman. Currently available on arXiv. In June 2019 I gave a recorded talk on this paper at the Banff International Research Station. Venkat gave a talk based on this work at ICERM in November 2018.
Robust Market Equilibria with Uncertain Preferences. With Christian Kroer, Alex Peysakhovich, and Parikshit Shah. To appear in the Thirty-Fourth AAAI Conference on Artificial Intelligence (AAAI-20).
Structured State Feedback for Metzler Dynamics. With James Anderson. Appeared in the 2018 IEEE Conference on Decision and Control (CDC).
Scheduling Distributed Clusters of Parallel Machines : Primal-Dual and LP-Based Algorithms. With Samir Khuller and Megan Chao. Appeared in the proceedings of the 24th European Symposium on Algorithms, in Aarhus, Denmark (2016). Extended version published in Algorithmica.