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.
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.
作者
胡珊珊
贺素香
Hu Shanshan;He Suxiang(Department of Mathematics,School of Science,Wuhan University of Technology,Wuhan 430070)
出处
《数学物理学报（A辑）》
CSCD
北大核心
2024年第2期500-512,共13页
Acta Mathematica Scientia
基金
国家自然科学基金(11871153)。
关键词
非负组稀疏约束优化问题
最优性条件
切锥
法锥
Non-negative group sparse constrained optimization
Optimality conditions
Tangent cone
Normal cone
