Date: Friday, March 23, 2018
Location: 1084 East Hall (4:10 PM to 5:00 PM)
Title: The Landscape of NonConvex Quadratic Feasibility
Abstract: Traditionally, a nonconvex problem is oftentimes solved by solving a convex approximation since finding the global minimizer of a convex problem is theoretically efficient. Unfortunately, there can be a mismatch between practice and theory since the convex optimization approach can be practically slow. On the other hand, solving the original nonconvex problem directly can be much faster in practice although in general, it is unclear whether these methods succeed since nonconvex functions can have many saddle points and local minima.
Recently, researchers have closed the gap theoretically in understanding why solving nonconvex problems directly reliably finds the global minimum. Under appropriate assumptions, in many important problemslike in matrix completion and simple neural networksthe reason for success is because every local minimum is a global minimum.
Motivated by this success and applications such as ordinal embedding and collaborative ranking, in this talk, we formulate homogeneous quadratic feasibility as an unconstrained, nonconvex minimization problem and aim to understand the landscape (local minimizers and global minimizers) of the nonconvex objective since the efficacy of applying a firstorder method like stochastic gradient descent hinges on the landscape. The only prerequisite of this talk is calculus.
Files:
Speaker: Amanda Bower
Institution: University of Michigan
Event Organizer: Audra McMillan amcm@umich.edu
