Sparse Quadratic Programs via Polynomial Roots

Algebra Student Seminar
Friday, September 23, 2022 - 10:00am for 1 hour (actually 50 minutes)
Skiles 006
Kevin Shu – Georgia Institute of Technology – kshu8@gatech.edu
Kevin Shu

We'll talk about problems of optimizing a quadratic function subject to quadratic constraints, in addition to a sparsity constraint that requires that solutions have only a few nonzero entries. Such problems include sparse versions of linear regression and principal components analysis. We'll see that this problem can be formulated as a convex conical optimization problem over a sparse version of the positive semidefinite cone, and then see how we can approximate such problems using ideas arising from the study of hyperbolic polynomials. We'll also describe a fast algorithm for such problems, which performs well in practical situations.