CMX Student/Postdoc Seminar
Convex relaxations and computational optimization
In this talk I give a tour of my work in convex relaxations for nonconvex problems, optimization modeling software, and some planned future work in numerical methods. I begin by introducing signomials and reviewing their history in optimization modeling for engineering design. Next, I show how the old idea of partial dualization can be revitalized with relative entropy optimization to develop an effective convex relaxation scheme for constrained signomial programming. I address in some detail how these signomial methods lead to advances in sparse and high-degree polynomial optimization, as well as new insights in convex and real-algebraic geometry. The second half of my talk shifts towards computational optimization. This shift begins by describing the SageOpt python package that implements the mathematics from my thesis, and proceeds by highlighting some of my contributions as one of three core developers of the widely-used CVXPY python package. I conclude by outlining possible uses of randomized numerical linear algebra and GPUs in second order methods for convex programming, and in particular I indicate how the latter method may help us solve operator relative entropy programs at scale.