Optimality Conditions for Group Sparse Constrained Optimization Problems

Wenying Wu and Dingtao Peng
Additional contact information
Wenying Wu: School of Mathematics and Statistics, Guizhou University, Guiyang 550025, China
Dingtao Peng: School of Mathematics and Statistics, Guizhou University, Guiyang 550025, China

Mathematics, 2021, vol. 9, issue 1, 1-17

Abstract: In this paper, optimality conditions for the group sparse constrained optimization (GSCO) problems are studied. Firstly, the equivalent characterizations of Bouligand tangent cone, Clarke tangent cone and their corresponding normal cones of the group sparse set are derived. Secondly, by using tangent cones and normal cones, four types of stationary points for GSCO problems are given: T B -stationary point, N B -stationary point, T C -stationary point and N C -stationary point, which are used to characterize first-order optimality conditions for GSCO problems. Furthermore, both the relationship among the four types of stationary points and the relationship between stationary points and local minimizers are discussed. Finally, second-order necessary and sufficient optimality conditions for GSCO problems are provided.

Keywords: group sparse constrained optimization; tangent cone; normal cone; first-order optimality condition; second-order optimality condition (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/9/1/84/pdf (application/pdf)
https://www.mdpi.com/2227-7390/9/1/84/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:9:y:2021:i:1:p:84-:d:473685

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().