On the Cyclic Barzilai-Borwein Stepsize Method for Unconstrained
Optimization
Yu-Hong Dai, W.W. Hager, K. Schittkowski,
Hongchao Zhang, IMA Journal on Numerical Analysis, Vol. 26, 604-627
(2006)
Abstract:
Due to its simplicity, efficiency, and extremely low memory requirements, the
Barzilai-Borwein (BB) gradient method has found many successful applications and
generalizations. In this paper, we will study the so-called cyclic
Barzilai-Borwein stepsize method, in which the same BB stepsize is used for
several consecutive iterations. Specifically, we provide some properties of this
method for strictly convex quadratic functions. After combining our new approach
with recently-established nonmonotone line search techniques, we develop an
adaptive cyclic BB stepsize algorithm for large-scale unconstrained
optimization. Our numerical experiments are based on the CUTE test problem
library and show that the adaptive algorithm is much better than the existing BB
gradient algorithm and is competitive with the well-known PRP+ conjugate
gradient algorithm.
To download a preprint, click here: cbb.pdf