James Anderson – Open positions

Columbia students – summer internship

Developing a Python sum-of-squares toolbox

Polynomial optimization and certifying non-negativity of multivariate polynomials a notoriously difficult problem. Despite the seemingly abstract nature of the problem, polynomial optimization has applications in many areas of engineering, computer science, physics, economics, combinatorics, and mathematics. The sum-of-squares decomposition is a sufficient condition for verifying non-negativity of a given polynomial. Parrilo's ground-breaking thesis showed that constructing a sum-of-squares decomposition can be formulated as a convex optimization problem, specifically a semidefinite program.

The freely available MATLAB toolbox, SOSTOOLS, allows us to formulate and solve sum-of-squares problems. Recently the Mathworks have updated their symbolic math engine and so SOSTOOLS needs to be updated. Instead of simply fixing the MATLAB implementation, this project will build a new version SOSTOOLS in python. In addition to recreating SOSTOOLS, we will also incorporate some of the latest methods that provide enhanced computational performance.

The ideal candidate for this project will be self-motivated, have experience coding in Python and MATLAB, and have taken a convex optimization class. If interested, please email me a CV, a link to a code repository (if applicable), and a brief description explaining why you think you would be a good fit for this project.

Applicants should email me at james.anderson@columbia.edu and include ‘‘Columbia student internship’’ in the subject line. Feel free to contact me with any questions.

Some useful references:

• SOSTOOLS website Don't be put off by the retro look of the site!

• Current user manual

• Survey paper

• Slides

Graduate students

If you're looking to do a PhD in electrical engineering, have a strong mathematical background, and are interested in some subset of distributed control theory, optimization, randomized numerical linear algebra, cyber-physical systems, or power networks, then please apply to the Columbia EE doctoral program here and list me as a potential advisor. The deadline for a Fall 2020 start is Dec 15th. Feel free to email me (ja3451@columbia.edu) with any questions. Send me your CV and we can discuss whether our interests are a good match.

Already admitted to Columbia? Drop me an email and we can talk about potential projects. I'll be on campus several times before I officially start in January.

Postdoc position

Potential postdocs… more info to follow soon.