| L1/2正则化问题的最优性条件及下降算法 |
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| 引用本文： | 吴磊,顾广泽. L1/2正则化问题的最优性条件及下降算法[J]. 湖南大学学报(自然科学版), 2013, 40(8): 114-118 |
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| 作者姓名： | 吴磊 顾广泽 |
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| 作者单位： | (湖南大学 数学与计量经济学院, 湖南 长沙410082) |
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| 摘 要： | 主要研究L1/2正则化问题.首先给出了该问题的最优性条件的分析,得到了一阶和二阶必要条件,同时给出了二阶充分条件.这些最优性条件可以看作是光滑函数最优性条件的推广.在此基础上,提出了一种下降算法,并给出了该算法的全局收敛性分析.该算法可以看作是最速下降法的推广.
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| 关 键 词： | 正则化 最优性条件 下降算法 全局收敛性 |
Optimality Conditions for the L1/2 Regularization Problem and a Descent Method |
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| Affiliation: | (College of Mathematics and Econometrics, Hunan Univ, Changsha, Hunan410082, China) |
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| Abstract: | This paper is concerned with the L1/2 regularization problem. We first study the optimality conditions for the problem. The optimality conditions obtained are the extensions of the optimality conditions for the minimization of a smooth function. Based on this, we derive a decent direction.We then develop a descent method for solving the problem. The method can be regarded as an extension of the well-known steepest descent method. Under appropriate conditions, we show that the proposed method is globally convergent. |
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| Keywords: | regularization problem optimality conditions descent method convergent |
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