| Monotone projected gradient methods for large-scale box-constrained quadratic programming |
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| 作者姓名： | ZHOU Bin GAO Li & DAI Yuhong School of Mathematical Sciences and LMAM Peking University Beijing China 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 Beijing China |
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| 作者单位： | ZHOU Bin，GAO Li & DAI Yuhong School of Mathematical Sciences and LMAM，Peking University，Beijing 100871，China; 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，Beijing 100080，China |
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| 摘 要： | Inspired by the success of the projected Barzilai-Borwein (PBB) method for large-scale box-constrained quadratic programming, we propose and analyze the monotone projected gradient methods in this paper. We show by experiments and analyses that for the new methods, it is generally a bad option to compute steplengths based on the negative gradients. Thus in our algorithms, some continuous or discontinuous projected gradients are used instead to compute the steplengths. Numerical experiments on a wide variety of test problems are presented, indicating that the new methods usually outperform the PBB method.
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| 收稿时间： | 11 May 2005 |
| 修稿时间： | 3 November 2005 |
Monotone projected gradient methods for large-scale box-constrained quadratic programming |
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| ZHOU Bin,GAO Li & DAI Yuhong School of Mathematical Sciences and LMAM,Peking University,Beijing ,China, 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,Beijing ,China.Monotone projected gradient methods for large-scale box-constrained quadratic programming[J].Science in China(Mathematics),2006,49(5):688-702. |
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| Authors: | ZHOU Bin GAO Li DAI Yuhong |
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| Institution: | 1. School of Mathematical Sciences and LMAM, Peking University, Beijing 100871, 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, Beijing 100080, China |
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| Abstract: | Inspired by the success of the projected Barzilai-Borwein (PBB) method for large-scale box-constrained quadratic programming, we propose and analyze the monotone projected gradient methods in this paper. We show by experiments and analyses that for the new methods, it is generally a bad option to compute steplengths based on the negative gradients. Thus in our algorithms, some continuous or discontinuous projected gradients are used instead to compute the steplengths. Numerical experiments on a wide variety of test problems are presented, indicating that the new methods usually outperform the PBB method. |
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| Keywords: | projected gradients monotone gradient methods box-constrained quadratic programming large-scale problems |
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