Optimality conditions for group sparsity constrained optimization problems with equality and inequality constraints

被引：0
作者：
Yi, Shouyu [1 ]
Peng, Dingtao [1 ,2 ]
Zhang, Xian [1 ]
机构：
[1] Guizhou Univ, Sch Math & Stat, Guiyang, Peoples R China
[2] Key Lab Game Decis & Control Syst Guizhou Prov, Guiyang, Peoples R China
来源：
OPTIMIZATION | 2025年
基金：
中国国家自然科学基金;
关键词：
Group sparsity constrained optimization; KKT point; constraint qualification; first-order optimality condition; second-order optimality condition; SELECTION;
D O I：
10.1080/02331934.2025.2487902
中图分类号：
C93 [管理学]; O22 [运筹学];
学科分类号：
070105 ; 12 ; 1201 ; 1202 ; 120202 ;
摘要：
The group sparsity constrained optimization problem with equality and inequality constraints (GSOP) refers to minimizing a given objective function while satisfying group sparsity constraints as well as equality and inequality constraints. By utilizing the constraint qualifications, we first derive the separability property of the Fr & eacute;chet, Mordukhovich and Clarke normal cones for the constraint set. Then, we introduce three categories of Karush-Kuhn-Tucker (KKT) points applicable to GSOP and obtain the corresponding optimality conditions using the separability of normal cones. Finally, the second-order optimality conditions for GSOP are provided. These results may provide some theoretical basis for analysing and solving the GSOPs.
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页数：32
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