Volume 12, 2007. 5 - 20. 
Zhiwei (Tony) Qin
The Relationships Between CG, BFGS, and two Limited-Memory Algorithms

Abstract For the solution of linear systems, the conjugate gradient (CG) and BFGS are among the most popular and successful algorithms with their respective advantages. The limited-memory methods have been developed to combine the best of the two. We describe and examine CG, BFGS, and two limited-memory methods (L-BFGS and VSCG) in the context of linear systems. We focus on the relationships between each of the four algorithms, and we present numerical results to illustrate those relationships.

Back To Volume Twelve Contents

Furman University Electronic Journal of Undergraduate Mathematics