Journal
IMA JOURNAL OF NUMERICAL ANALYSIS
Volume 26, Issue 3, Pages 604-627Publisher
OXFORD UNIV PRESS
DOI: 10.1093/imanum/drl006
Keywords
unconstrained optimization; gradient method; convex quadratic programming; non-monotone line search
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In the cyclic Barzilai-Borwein (CBB) method, the same Barzilai-Borwein (BB) stepsize is reused for m consecutive iterations. It is proved that CBB is locally linearly convergent at a local minimizer with positive definite Hessian. Numerical evidence indicates that when m > n/2 >= 3, where n is the problem dimension, CBB is locally superlinearly convergent. In the special case m = 3 and n = 2, it is proved that the convergence rate is no better than linear, in general. An implementation of the CBB method, called adaptive cyclic Barzilai-Borwein (ACBB), combines a non-monotone line search and an adaptive choice for the cycle length m. In numerical experiments using the CUTEr test problem library, ACBB performs better than the existing BB gradient algorithm, while it is competitive with the well-known PRP+ conjugate gradient algorithm.
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