| 一类不可微规划算法的线性收敛性 |
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| 引用本文： | 郑颖春,王雪峰.一类不可微规划算法的线性收敛性[J].西北轻工业学院学报,2013(3):154-156,170. |
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| 作者姓名： | 郑颖春 王雪峰 |
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| 作者单位： | 西安科技大学理学院 |
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| 基金项目： | 国家自然科学基金项目(71103143) |
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| 摘 要： | 介绍了一类不可微优化的次梯度算法，并结合文献9]，给出了次梯度算法的简化形式；通过引进二阶方向导数的概念，证明了不可微函数的一阶及二阶积分中值定理，这些中值定理和可微函数的中值定理是类似的；利用这些中值定理，借助文献9]的证明方法，证明了一般的次梯度算法都具有线性收敛性．
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| 关 键 词： | 不可微规划 算法 线性收敛性 |
The linear convergence nondifferentiable of an algorithm for programming |
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| ZHENG Ying-chun,WANG Xue-feng.The linear convergence nondifferentiable of an algorithm for programming[J].Journal of Northwest University of Light Industry,2013(3):154-156,170. |
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| Authors: | ZHENG Ying-chun WANG Xue-feng |
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| Affiliation: | (College of science,Xi′an University of Science & Technology,Xi′an 710054,China) |
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| Abstract: | This paper introduces a kind of sub-gradient algorithm, and combining with docu- ment9],given simplified form of the sub-gradient algorithm by introducing the concept of second order directional derivative, proved first and second order integral mean value theo- rem of the nondiffenrentiable function,The mean value theorem and the mean value theorem of differentiable functions is similar; by the mean value theorem,with the help of the method of document9],we proof that the general sub-gradient algorithm has linear convergence. |
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| Keywords: | nondifferentiable optimization aIgorithm linear convergence |
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