| 基于KKT条件的稀疏编码算法收敛性研究 |
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| 引用本文： | 陶盈吟,杨仪,代祥光,苏晓杰. 基于KKT条件的稀疏编码算法收敛性研究[J]. 南京气象学院学报, 2020, 12(3): 360-363 |
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| 作者姓名： | 陶盈吟 杨仪 代祥光 苏晓杰 |
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| 作者单位： | 重庆三峡学院 智能信息处理与控制重庆高校市级重点实验室, 重庆, 404100,重庆三峡学院 智能信息处理与控制重庆高校市级重点实验室, 重庆, 404100,重庆三峡学院 智能信息处理与控制重庆高校市级重点实验室, 重庆, 404100,重庆大学 自动化学院, 重庆, 400044 |
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| 基金项目： | 重庆市高校市级重点实验室资助项目（[2017]3）；重庆市发展和改革委员会资助项目（2017[1007]）；重庆市教委科技研究项目（KJQN201901203，KJQN201901218，KJ1710248）；重庆市自然科学基金（cstc2019jcyj-bshX0101） |
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| 摘 要： | 本文提出了基于KKT条件的稀疏编码算法.首先，将非凸非光滑的稀疏编码问题分解成两个凸非光滑问题；然后，巧妙地运用两个矩阵使两个凸非光滑问题转换成三个光滑凸优化问题，并通过KKT条件对三个问题进行求解，再通过凸优化理论证明三个问题在其对应规则下是非增的.最后，实验结果验证了算法的收敛性.
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| 关 键 词： | KKT条件 收敛性 非凸非光滑 稀疏编码 |
| 收稿时间： | 2020-02-26 |
Convergence of sparse coding based on KKT conditions |
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| TAO Yingyin,YANG Yi,DAI Xiangguang and SU Xiaojie. Convergence of sparse coding based on KKT conditions[J]. Journal of Nanjing Institute of Meteorology, 2020, 12(3): 360-363 |
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| Authors: | TAO Yingyin YANG Yi DAI Xiangguang SU Xiaojie |
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| Affiliation: | Key Laboratory of Intelligent Information Processing and Control of Chongqing Municipal Institutions of Higher Education, Chongqing Three Gorges University, Chongqing 404100,Key Laboratory of Intelligent Information Processing and Control of Chongqing Municipal Institutions of Higher Education, Chongqing Three Gorges University, Chongqing 404100,Key Laboratory of Intelligent Information Processing and Control of Chongqing Municipal Institutions of Higher Education, Chongqing Three Gorges University, Chongqing 404100 and College of Automation, Chongqing University, Chongqing 400044 |
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| Abstract: | This paper proposes a sparse coding algorithm based on KKT conditions.Firstly,the non-convex non-smooth sparse coding problem is decomposed into two convex non-smooth problems.Secondly,the two convex non-smooth problems are skillfully transformed into three smooth convex optimization problems by using two matrices.Finally,the three problems are solved by KKT conditions.In addition,we prove the convergence of the algorithm.Meanwhile,experimental simulation shows the convergence of the algorithm. |
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| Keywords: | KKT conditions convergence non-convex non-mooth sparse coding |
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