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Zbl 1121.90099
Zhou, Bin; Gao, Li; Dai, Yu-Hong
Gradient methods with adaptive step-sizes. (English)
[J] Comput. Optim. Appl. 35, No. 1, 69-86 (2006). ISSN 0926-6003; ISSN 1573-2894/e

Summary: 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.

MSC 2000:: *90C20 Quadratic programming
90C52 Methods of reduced gradient type

Keywords: linear system; gradient method; adaptive step-size; Barzilai-Borwein method; superlinear behavior; trust-region approach

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