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.

## PhD Thesis

Applications of convex analysis to signomial and polynomial nonnegativity problems. [CaltechTHESIS record, PDF].

*Received the Amori Doctoral Prize in Computing and Mathematical Sciences.*

This thesis combines (and slightly expands upon) four papers I wrote in graduate school. The new content includes applications in chemical reaction networks and more discussion of the sageopt python package. There is also a chapter on preliminaries that covers generic ideas like nonnegativity cones, moment relaxations, and convex cone programming. This is an excellent on-boarding resource to learn about sums of arithmetic-geometric exponentials (SAGE) and related ideas such as sums of nonnegative circuits (SONC).

## Preprints

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).

## Publications

**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.

**Robust Market Equilibria with Uncertain Preferences**. With Christian Kroer, Alex Peysakhovich, and Parikshit Shah. [arXiv, AAAI 2020, blog post].

**Structured State Feedback for Metzler Dynamics***. *With James Anderson. [CDC 2018].

**Scheduling Distributed Clusters of Parallel Machines : Primal-Dual and LP-Based Algorithms***. *With Samir Khuller and Megan Chao. [arXiv, ESA 2016, extended version in Algorithmica].