非负组稀疏约束优化问题的最优性条件

数学物理学报 ›› 2024, Vol. 44 ›› Issue (2): 500-512.

• • 上一篇

非负组稀疏约束优化问题的最优性条件

胡珊珊(),贺素香^*()

武汉理工大学理学院数学系武汉 430070

收稿日期:2022-12-26 修回日期:2023-06-01 出版日期:2024-04-26 发布日期:2024-04-07
通讯作者: * 贺素香, Email:hesux@whut.edu.cn
作者简介:胡珊珊,Email:1515034317@qq.com
基金资助:
国家自然科学基金(11871153)

Optimality Conditions for Non-Negative Group Sparse Constrained Optimization Problems

Hu Shanshan(),He Suxiang^*()

Department of Mathematics, School of Science, Wuhan University of Technology, Wuhan 430070

Received:2022-12-26 Revised:2023-06-01 Online:2024-04-26 Published:2024-04-07
Supported by:
NSFC(11871153)

摘要/Abstract

摘要：

基于 Bouligand 意义下的切锥与法锥和 Clarke 意义下的切锥与法锥, 该文研究了非负组稀疏约束优化问题的最优性理论. 该文定义了非负组稀疏约束集的 Bouligand 切锥与法锥和 Clarke 切锥与法锥, 并给出了它们的等价刻画形式. 在目标函数连续可微的条件下, 借助于非负组稀疏约束集的切锥和法锥, 给出了该优化问题的四类稳定点的定义, 并讨论了它们之间的关系. 最后, 建立了非负组稀疏约束优化问题的一阶和二阶最优性条件.

关键词: 非负组稀疏约束优化问题, 最优性条件, 切锥, 法锥

Abstract:

Based on the Bouligand tangent cone, Clarke tangent cone and their corresponding normal cones, the optimality theories of the non-negative group sparse constrained optimization problem are studied. This paper defines the Bouligand tangent cone and its normal cone and the Clarke tangent cone and its normal cone of the non-negative group sparse constraint set, and presents their equivalent characterizations. Under the assumption that the objective function is continuously differentiable, with the help of the tangent cone and the normal cone of the sparse constrained set of the non-negative group, the definitions of four types of stable points for the optimization problem are given and the relationships between these four types of stable points are discussed. Finally, the first-order and second-order optimality conditions for the optimization problem of sparse constraint of non-negative groups are established.

Key words: Non-negative group sparse constrained optimization, Optimality conditions, Tangent cone, Normal cone

中图分类号:

O224

胡珊珊, 贺素香. 非负组稀疏约束优化问题的最优性条件[J]. 数学物理学报, 2024, 44(2): 500-512.

Hu Shanshan, He Suxiang. Optimality Conditions for Non-Negative Group Sparse Constrained Optimization Problems[J]. Acta mathematica scientia,Series A, 2024, 44(2): 500-512.

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非负组稀疏约束优化问题的最优性条件

Optimality Conditions for Non-Negative Group Sparse Constrained Optimization Problems

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