Gradient Methods with Adaptive Step-Sizes |
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Authors: | Bin Zhou Li Gao Yu-Hong Dai |
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Institution: | (1) School of Mathematical Sciences and LMAM, Peking University, Beijing, 100871, People’s Republic of China;(2) State Key Laboratory of Scientific and Engineering Computing, Institute of Computational Mathematics and Scientific/Engineering Computing, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, P. O. Box 2719, Beijing, 100080, People’s Republic of China |
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Abstract: | Motivated by the superlinear behavior of the Barzilai-Borwein (BB) method for two-dimensional quadratics, we propose two gradient
methods which adaptively choose a small step-size or a large step-size at each iteration. The small step-size is primarily
used to induce a favorable descent direction for the next iteration, while the large step-size is primarily used to produce
a sufficient reduction. Although the new algorithms are still linearly convergent in the quadratic case, numerical experiments
on some typical test problems indicate that they compare favorably with the BB method and some other efficient gradient methods. |
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Keywords: | linear system gradient method adaptive step-size Barzilai-Borwein method superlinear behavior trust-region approach |
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