Research

I’m currently working on randomized numerical linear algebra (RandNLA). Specifically, I’m leading the development of an LAPACK-like library for RandNLA as part of BALLISTIC.

I started contributing to CVXPY starting in January 2018. I now serve on the CVXPY steering committee and as one of its five project maintainers.

Preprints

Randomized Numerical Linear Algebra: A Perspective on the Field With an Eye to Software.

I’m the lead author of this 200-page monograph. It has a total of 13 authors, including Michael Mahoney, James Demmel, and Jack Dongarra. Check it out on arXiv!

Publications

My thesis work focused 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.

Algebraic Perspectives on Signomial Optimization.

With Mareike Dressler. Published in the SIAM Journal on Applied Algebra and Geometry. A slightly older version is available on arXiv. An early-still version of this work appears as Chapter 6 of my PhD thesis.

Sublinear Circuits and the Constrained Signomial Nonnegativity Problem.

With Helen Naumann and Thorsten Theobald. Currently available open-access at Mathematical Programming (2022). The same content is covered in a slightly more digestible way in Chapter 5 of my PhD thesis.

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 that 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. The material in this paper appears (in expanded forms) throughout Chapters 4, 7, and 8 of my PhD thesis.

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. The material in this paper appears in Chapter 3 of my PhD thesis.

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].

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).