My area of research is mathematical optimization. For the last three 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. The mathematical techniques I have developed are implemented in the comprehensive sageopt python package. I have developing interests in applied algebraic geometry and second-order methods for constrained convex optimization. In parallel with these efforts I’ve regularly contributed to CVXPY, and I currently serve as one of three members of CVXPY’s core development team.
Sublinear Circuits and the Constrained Signomial Nonnegativity Problem
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. Available at Mathematical Programming Computation (2020) , with an earlier version on arXiv (2019). 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. Errata.
Newton Polytopes and Relative Entropy Optimization.
With Venkat Chandrasekaran and Adam Wierman. Available at Foundations of Computational Mathematics (2021). You can find a freely available read-only copy from Springer at this link (see also 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.
Structured State Feedback for Metzler Dynamics. With James Anderson. [CDC 2018].