R-linear convergence of the Barzilai and Borwein gradient method |
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| Authors: | Dai Yu-Hong; Liao Li-Zhi |
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| Institution: |
1 State Key Laboratory of Scientific and Engineering Computing, Institute of Computational Mathematics and Scientific/Engineering Computing, Academy of Mathematics and Systems Sciences, Chinese Academy of Sciences, PO Box 2719, Beijing 100080, People's Republic of China 2 Department of Mathematics, Hong Kong Baptist University, Kowloon Tong, Kowloon, Hong Kong, People's Republic of China
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| Abstract: | Combined with non-monotone line search, the Barzilai and Borwein(BB) gradient method has been successfully extended for solvingunconstrained optimization problems and is competitive withconjugate gradient methods. In this paper, we establish theR-linear convergence of the BB method for any-dimensional stronglyconvex quadratics. One corollary of this result is that theBB method is also locally R-linear convergent for general objectivefunctions, and hence the stepsize in the BB method will alwaysbe accepted by the non-monotone line search when the iterateis close to the solution. |
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| Keywords: | unconstrained optimization gradient method R-linear convergence strictly convex |
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