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| L_1正则化问题的对偶性理论 | |
| 引用本文： | 吴焚供. L_1正则化问题的对偶性理论[J]. 中山大学学报(自然科学版), 2015, 54(1) |
| 作者姓名： | 吴焚供 |
| 作者单位： | 1. 华南师范大学数学科学学院,广州 广东 510631; 2. 广东第二师范学院数学系,广州 广东 510303 |
| 基金项目： | 广东省教育厅科研项目“育苗工程”(自然科学)资助项目 |
| 摘 要： | L1正则化问题是一个非光滑的无约束最优化问题,在变量选择,数据压缩和图像处理等领域有广泛的应用。给出了L1问题最优解存在的新的必要条件和充分条件,利用这些条件构造出L1正则化问题的一个MondWeir型对偶问题,最后给出了相应的弱对偶定理和强对偶定理。 |
| 关 键 词： | L1 正则化 最优解 对偶问题 |
Duality Theorem for L1-Regularization Problem |
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| WU Fengong. Duality Theorem for L1-Regularization Problem[J]. Acta Scientiarum Naturalium Universitatis Sunyatseni, 2015, 54(1) | |
| Authors: | WU Fengong |
| Affiliation: | 1. Department of Mathematics, South China Normal University, Guangzhou 510631, China; 2. Department of Mathematics, Guangdong University of Education, Guangzhou 510303, China |
| Abstract: | L1 regularization problem is a non-smooth unconstrained optimization problem,which is widely used in the fields such as variable selection,data compression and image processing. Optimality conditions for the solution of L1 regularization problem is given. And a Mond Weir type dual problem for L1 regularization problem is formulated, by using these optimal conditions. Finally a weak duality theorem and a strong duality theorem are proved. |
| Keywords: | L1 -regularization optimality condition dual problem |
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