| 求解界约束优化的一种新的非单调谱投影梯度法 |
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| 引用本文： | 毕亚倩,刘新为. 求解界约束优化的一种新的非单调谱投影梯度法[J]. 计算数学, 2013, 35(4): 419-430 |
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| 作者姓名： | 毕亚倩 刘新为 |
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| 作者单位： | 河北工业大学理学院, 天津 300401 |
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| 基金项目： | 国家自然科学基金资助项目（11271107）。 |
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| 摘 要： | 本文给出求解界约束优化问题的一种新的非单调谱投影梯度算法. 该算法是将谱投影梯度算法与Zhang and Hager [SIAM Journal on Optimization，2004，4（4）：1043-1056]提出的非单调线搜索结合得到的方法. 在合理的假设条件下，证明了算法的全局收敛性.数值实验结果表明，与已有的界约束优化问题的谱投影梯度法比较，利用本文给出的算法求解界约束优化问题是有竞争力的.
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| 关 键 词： | 界约束优化问题 非单调线搜索 谱投影梯度法 全局收敛 |
| 收稿时间： | 2013-04-22; |
A NEW NONMONOTONE SPECTRAL PROJECTED GRADIENT METHOD FOR BOUND CONSTRAINED OPTIMIZATION |
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| Bi Yaqian,Liu Xinwei. A NEW NONMONOTONE SPECTRAL PROJECTED GRADIENT METHOD FOR BOUND CONSTRAINED OPTIMIZATION[J]. Mathematica Numerica Sinica, 2013, 35(4): 419-430 |
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| Authors: | Bi Yaqian Liu Xinwei |
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| Affiliation: | School of Science, Hebei University of Technology, Tianjin 300401, China |
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| Abstract: | A new nonmonotone spectral projected gradient method for bound constrained optimization problems is presented. The method is developed by combining the spectral projected gradient method with a nonmonotone line search technique which is presented by Zhang and Hager [SIAM Journal on Optimization, 2004, 14(4): 1043-1056]. Under mild conditions, the method is proved to be globally convergent. Compared with the existing spectral projected gradient methods, our numerical tests show that the presented method here is more competitive. |
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| Keywords: | bound constrained optimization nonmonotone line search spectral projected gradient method global convergence |
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