A Low-Cost Alternating Projection Approach for a Continuous Formulation of Convex and Cardinality Constrained Optimization

Detalhes bibliográficos
Autor(a) principal: Krejić, N.
Data de Publicação: 2023
Outros Autores: Krulikovski, E. H. M., Raydan, M.
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
Texto Completo: http://hdl.handle.net/10362/164090
Resumo: Funding Information: Open access funding provided by FCT|FCCN (b-on). The first author was financially supported by the Serbian Ministry of Education, Science, and Technological Development and Serbian Academy of Science and Arts, grant no. F10. 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 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). Publisher Copyright: © 2023, The Author(s).
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spelling A Low-Cost Alternating Projection Approach for a Continuous Formulation of Convex and Cardinality Constrained Optimization65K0590C3091G1091G15Cardinality constraintsDykstra’s algorithmEfficient frontierPortfolio optimizationProjected gradient methodsEconomics, Econometrics and Finance (miscellaneous)Computer Science ApplicationsControl and OptimizationApplied MathematicsFunding Information: Open access funding provided by FCT|FCCN (b-on). The first author was financially supported by the Serbian Ministry of Education, Science, and Technological Development and Serbian Academy of Science and Arts, grant no. F10. 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 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). Publisher Copyright: © 2023, The Author(s).We consider convex constrained optimization problems that also include a cardinality constraint. In general, optimization problems with cardinality constraints are difficult mathematical programs which are usually solved by global techniques from discrete optimization. We assume that the region defined by the convex constraints can be written as the intersection of a finite collection of convex sets, such that it is easy and inexpensive to project onto each one of them (e.g., boxes, hyper-planes, or half-spaces). Taking advantage of a recently developed continuous reformulation that relaxes the cardinality constraint, we propose a specialized penalty gradient projection scheme combined with alternating projection ideas to compute a solution candidate for these problems, i.e., a local (possibly non-global) solution. To illustrate the proposed algorithm, we focus on the standard mean-variance portfolio optimization problem for which we can only invest in a preestablished limited number of assets. For these portfolio problems with cardinality constraints, we present a numerical study on a variety of data sets involving real-world capital market indices from major stock markets. In many cases, we observe that the proposed scheme converges to the global solution. On those data sets, we illustrate the practical performance of the proposed scheme to produce the effective frontiers for different values of the limited number of allowed assets.CMA - Centro de Matemática e AplicaçõesRUNKrejić, N.Krulikovski, E. H. M.Raydan, M.2024-02-24T00:22:15Z2023-122023-12-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/article24application/pdfhttp://hdl.handle.net/10362/164090engPURE: 83893960https://doi.org/10.1007/s43069-023-00257-winfo:eu-repo/semantics/openAccessreponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãoinstacron:RCAAP2024-03-11T05:50:46Zoai:run.unl.pt:10362/164090Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-20T04:00:02.896306Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãofalse
dc.title.none.fl_str_mv A Low-Cost Alternating Projection Approach for a Continuous Formulation of Convex and Cardinality Constrained Optimization
title A Low-Cost Alternating Projection Approach for a Continuous Formulation of Convex and Cardinality Constrained Optimization
spellingShingle A Low-Cost Alternating Projection Approach for a Continuous Formulation of Convex and Cardinality Constrained Optimization
Krejić, N.
65K05
90C30
91G10
91G15
Cardinality constraints
Dykstra’s algorithm
Efficient frontier
Portfolio optimization
Projected gradient methods
Economics, Econometrics and Finance (miscellaneous)
Computer Science Applications
Control and Optimization
Applied Mathematics
title_short A Low-Cost Alternating Projection Approach for a Continuous Formulation of Convex and Cardinality Constrained Optimization
title_full A Low-Cost Alternating Projection Approach for a Continuous Formulation of Convex and Cardinality Constrained Optimization
title_fullStr A Low-Cost Alternating Projection Approach for a Continuous Formulation of Convex and Cardinality Constrained Optimization
title_full_unstemmed A Low-Cost Alternating Projection Approach for a Continuous Formulation of Convex and Cardinality Constrained Optimization
title_sort A Low-Cost Alternating Projection Approach for a Continuous Formulation of Convex and Cardinality Constrained Optimization
author Krejić, N.
author_facet Krejić, N.
Krulikovski, E. H. M.
Raydan, M.
author_role author
author2 Krulikovski, E. H. M.
Raydan, M.
author2_role author
author
dc.contributor.none.fl_str_mv CMA - Centro de Matemática e Aplicações
RUN
dc.contributor.author.fl_str_mv Krejić, N.
Krulikovski, E. H. M.
Raydan, M.
dc.subject.por.fl_str_mv 65K05
90C30
91G10
91G15
Cardinality constraints
Dykstra’s algorithm
Efficient frontier
Portfolio optimization
Projected gradient methods
Economics, Econometrics and Finance (miscellaneous)
Computer Science Applications
Control and Optimization
Applied Mathematics
topic 65K05
90C30
91G10
91G15
Cardinality constraints
Dykstra’s algorithm
Efficient frontier
Portfolio optimization
Projected gradient methods
Economics, Econometrics and Finance (miscellaneous)
Computer Science Applications
Control and Optimization
Applied Mathematics
description Funding Information: Open access funding provided by FCT|FCCN (b-on). The first author was financially supported by the Serbian Ministry of Education, Science, and Technological Development and Serbian Academy of Science and Arts, grant no. F10. 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 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). Publisher Copyright: © 2023, The Author(s).
publishDate 2023
dc.date.none.fl_str_mv 2023-12
2023-12-01T00:00:00Z
2024-02-24T00:22:15Z
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
dc.type.driver.fl_str_mv info:eu-repo/semantics/article
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status_str publishedVersion
dc.identifier.uri.fl_str_mv http://hdl.handle.net/10362/164090
url http://hdl.handle.net/10362/164090
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv PURE: 83893960
https://doi.org/10.1007/s43069-023-00257-w
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
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application/pdf
dc.source.none.fl_str_mv reponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
instacron:RCAAP
instname_str Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
instacron_str RCAAP
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reponame_str Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
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repository.name.fl_str_mv Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
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