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

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