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.
The X-Circuits Behind Conditional SAGE Certificates
With Helen Naumann and Thorsten Theobald. Currently available on arXiv. I mentioned this work towards the end of my MIT vsOPT talk. I also have slides from a 30 minute presentation focused on the paper (notation in slides is slightly different from the paper).
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 have two sets of slides which address the whole paper (MPI MiS 2019, ICCOPT 2019). On April 17 2020 I gave a recorded talk through MIT, which addressed the signomial parts of the paper in detail, along with other recent results in this area.
To appear in Mathematical Programming Computation.
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. [arXiv, to appear in AAAI 2020].
Structured State Feedback for Metzler Dynamics. With James Anderson. [CDC 2018].