Quasi-Newton Trust-Region Methods

Quasi-Newton methods are viable alternatives to Newton’s method for solving optimization problems because they do not require computing and solving with the potentially very large Hessian matrix while still maintaining a superlinear convergence rate. Systems of linear equations arising from quasi-Newton methods can be solved efficiently using the compact representation of the quasi-Newton matrices. In this talk, we present a compact formulation for the entire Broyden convex class of updates for limited-memory quasi-Newton methods. Furthermore, we demonstrate how they can be used to solve large-scale trust-region subproblems with quasi-Newton Hessian approximations.

Joint work with Jennifer Erway (Wake Forest University) and Johannes Brust (UC Merced)
http://faculty.ucmerced.edu/rmarcia/index.html