TY - JOUR
T1 - An augmented Lagrangian approach for cardinality constrained minimization applied to variable selection problems
AU - Krejić, N.
AU - Krulikovski, E. H. M.
AU - Raydan, M.
N1 - Funding Information:
info:eu-repo/grantAgreement/FCT/Concurso para Financiamento de Projetos de Investigação Científica e Desenvolvimento Tecnológico em Todos os Domínios Científicos - 2020/PTDC%2FCCI-BIO%2F4180%2F2020/PT#
The first author was financially supported by the Provincial Secretariat for Higher Education and Scientific Research of Vojvodina , grant number 142-451-2593/2021-01/2 . The second author was financially supported by Fundação para a Ciência e a Tecnologia (FCT) (Portuguese Foundation for Science and Technology) under the scope of the projects UIDB/MAT/00297/2020 , UIDP/MAT/00297/2020 (Centro de Matemática e Aplicações), and UI/297/2020-5/2021 . The third author was financially supported by the Fundação para a Ciência e a Tecnologia (Portuguese Foundation for Science and Technology) under the scope of the projects UIDB/MAT/00297/2020 and UIDP/MAT/00297/2020 (Centro de Matemática e Aplicações).
Publisher Copyright:
© 2023 The Author(s)
PY - 2023
Y1 - 2023
N2 - To solve convex constrained minimization problems, that also include a cardinality constraint, we propose an augmented Lagrangian scheme combined with alternating projection ideas. Optimization problems that involve a cardinality constraint are NP-hard mathematical programs and typically very hard to solve approximately. Our approach takes advantage of a recently developed and analyzed continuous formulation that relaxes the cardinality constraint. Based on that formulation, we solve a sequence of smooth convex constrained minimization problems, for which we use projected gradient-type methods. In our setting, the convex constraint region can be written as the intersection of a finite collection of convex sets that are easy and inexpensive to project. We apply our approach to a variety of over and under determined constrained linear least-squares problems, with both synthetic and real data that arise in variable selection, and demonstrate its effectiveness.
AB - To solve convex constrained minimization problems, that also include a cardinality constraint, we propose an augmented Lagrangian scheme combined with alternating projection ideas. Optimization problems that involve a cardinality constraint are NP-hard mathematical programs and typically very hard to solve approximately. Our approach takes advantage of a recently developed and analyzed continuous formulation that relaxes the cardinality constraint. Based on that formulation, we solve a sequence of smooth convex constrained minimization problems, for which we use projected gradient-type methods. In our setting, the convex constraint region can be written as the intersection of a finite collection of convex sets that are easy and inexpensive to project. We apply our approach to a variety of over and under determined constrained linear least-squares problems, with both synthetic and real data that arise in variable selection, and demonstrate its effectiveness.
KW - Augmented Lagrangian method
KW - Cardinality constraints
KW - Constrained linear least-squares
KW - Variable selection
UR - http://www.scopus.com/inward/record.url?scp=85180587145&partnerID=8YFLogxK
U2 - 10.1016/j.apnum.2023.12.006
DO - 10.1016/j.apnum.2023.12.006
M3 - Article
AN - SCOPUS:85180587145
SN - 0168-9274
JO - Applied Numerical Mathematics
JF - Applied Numerical Mathematics
ER -