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Thesis Defense - Lu

A Study of the Limited Memory SR1 Method in Practice
Xuehua Lu
Computer Science PhD Candidate

Limited Memory BFGS method (L-BFGS) has been shown to be an effective way to solve large scale optimization problems. Generally, an m-step Limited Memory method is essentially a quasi-Newton method where only m of the updates to the nXn Hessian approximation are stored (m<<n).

In this dissertation, we present an implementation of the Limited Memory Symmetric Rank One method (L-SR1) with the assistance of the compact representation of SR1 updates. Our numerical experiments indicate that the performance of L-SR1 method is sensitive to the initial scaling parameter and with our special choice, it can perform comparably with the L-BFGS method. We also prove the global and Q-linear local convergence, which is actually true for any Hessian approximations as long as they are uniformly bounded.

Committee: Richard Byrd, Professor (Chair)
Xiao-Chuan Cai, Assistant Professor
Elizabeth Jessup, Assistant Professor
Robert (Bobby) Schnabel, Professor
Gregory Beylkin, Department of Applied Mathematics
Department of Computer Science
University of Colorado Boulder
Boulder, CO 80309-0430 USA
May 5, 2012 (14:20)