Publicação
A global hybrid derivative-free method for high-dimensional systems of nonlinear equations
| Resumo: | This work concerns the numerical solution of high-dimensional systems of nonlinear equations, when derivatives are not available for use, but assuming that all functions defining the problem are continuously differentiable. A hybrid approach is taken, based on a derivative-free iterative method, organized in two phases. The first phase is defined by derivative-free versions of a fixed-point method that employs spectral parameters to define the steplength along the residual direction. The second phase consists on a matrix-free inexact Newton method that employs the Generalized Minimal Residual algorithm to solve the linear system that computes the search direction. This second phase will only take place if the first one fails to find a better point after a predefined number of reductions in the step size. In all stages, the criterion to accept a new point considers a nonmonotone decrease condition upon a merit function. Convergence results are established and the numerical performance is assessed through experiments in a set of problems collected from the literature. Both the theoretical and the experimental analysis support the feasibility of the proposed hybrid strategy. |
|---|---|
| Autores principais: | Begiato, Rodolfo G. |
| Outros Autores: | Custódio, Ana Luisa; Gomes-Ruggiero, Márcia A. |
| Assunto: | Derivative-free optimization methods Inexact Newton Nonlinear systems of equations Nonmonotone line search Spectral residual Control and Optimization Computational Mathematics Applied Mathematics |
| Ano: | 2020 |
| País: | Portugal |
| Tipo de documento: | artigo |
| Tipo de acesso: | acesso aberto |
| Instituição associada: | Universidade Nova de Lisboa |
| Idioma: | inglês |
| Origem: | Repositório Institucional da UNL |
| _version_ | 1868415136949075968 |
|---|---|
| author | Begiato, Rodolfo G. |
| author2 | Custódio, Ana Luisa Gomes-Ruggiero, Márcia A. |
| author2_role | author author |
| author_facet | Begiato, Rodolfo G. Custódio, Ana Luisa Gomes-Ruggiero, Márcia A. |
| author_role | author |
| contributor_name_str_mv | DM - Departamento de Matemática CMA - Centro de Matemática e Aplicações Springer Science Business Media RUN |
| country_str | PT |
| creators_json_txt | [{\"Person.name\":\"Begiato, Rodolfo G.\"},{\"Person.name\":\"Custódio, Ana Luisa\"},{\"Person.name\":\"Gomes-Ruggiero, Márcia A.\"}] |
| datacite.contributors.contributor.contributorName.fl_str_mv | DM - Departamento de Matemática CMA - Centro de Matemática e Aplicações Springer Science Business Media RUN |
| datacite.creators.creator.creatorName.fl_str_mv | Begiato, Rodolfo G. Custódio, Ana Luisa Gomes-Ruggiero, Márcia A. |
| datacite.date.Accepted.fl_str_mv | 2020-01-01T00:00:00Z |
| datacite.date.available.fl_str_mv | 2021-04-26T22:55:03Z |
| datacite.date.embargoed.fl_str_mv | 2021-04-26T22:55:03Z |
| datacite.rights.fl_str_mv | http://purl.org/coar/access_right/c_abf2 |
| datacite.subjects.subject.fl_str_mv | Derivative-free optimization methods Inexact Newton Nonlinear systems of equations Nonmonotone line search Spectral residual Control and Optimization Computational Mathematics Applied Mathematics |
| datacite.titles.title.fl_str_mv | A global hybrid derivative-free method for high-dimensional systems of nonlinear equations |
| dc.contributor.none.fl_str_mv | DM - Departamento de Matemática CMA - Centro de Matemática e Aplicações Springer Science Business Media RUN |
| dc.creator.none.fl_str_mv | Begiato, Rodolfo G. Custódio, Ana Luisa Gomes-Ruggiero, Márcia A. |
| dc.date.Accepted.fl_str_mv | 2020-01-01T00:00:00Z |
| dc.date.available.fl_str_mv | 2021-04-26T22:55:03Z |
| dc.date.embargoed.fl_str_mv | 2021-04-26T22:55:03Z |
| dc.format.none.fl_str_mv | application/pdf |
| dc.identifier.none.fl_str_mv | http://hdl.handle.net/10362/116219 |
| dc.language.none.fl_str_mv | eng |
| dc.rights.none.fl_str_mv | http://purl.org/coar/access_right/c_abf2 |
| dc.subject.none.fl_str_mv | Derivative-free optimization methods Inexact Newton Nonlinear systems of equations Nonmonotone line search Spectral residual Control and Optimization Computational Mathematics Applied Mathematics |
| dc.title.fl_str_mv | A global hybrid derivative-free method for high-dimensional systems of nonlinear equations |
| dc.type.none.fl_str_mv | http://purl.org/coar/resource_type/c_6501 |
| description | This work concerns the numerical solution of high-dimensional systems of nonlinear equations, when derivatives are not available for use, but assuming that all functions defining the problem are continuously differentiable. A hybrid approach is taken, based on a derivative-free iterative method, organized in two phases. The first phase is defined by derivative-free versions of a fixed-point method that employs spectral parameters to define the steplength along the residual direction. The second phase consists on a matrix-free inexact Newton method that employs the Generalized Minimal Residual algorithm to solve the linear system that computes the search direction. This second phase will only take place if the first one fails to find a better point after a predefined number of reductions in the step size. In all stages, the criterion to accept a new point considers a nonmonotone decrease condition upon a merit function. Convergence results are established and the numerical performance is assessed through experiments in a set of problems collected from the literature. Both the theoretical and the experimental analysis support the feasibility of the proposed hybrid strategy. |
| dirty | 0 |
| eu_rights_str_mv | openAccess |
| format | article |
| fulltext.url.fl_str_mv | https://run.unl.pt/bitstreams/fe0a0042-aec0-4ab1-9b3e-aa2f610538cf/download |
| id | run_87d7dac98ab4e76e9744641dabcd179f |
| identifier.url.fl_str_mv | http://hdl.handle.net/10362/116219 |
| instacron_str | unl |
| institution | Universidade Nova de Lisboa |
| instname_str | Universidade Nova de Lisboa |
| language | eng |
| network_acronym_str | run |
| network_name_str | Repositório Institucional da UNL |
| oai_identifier_str | oai:run.unl.pt:10362/116219 |
| organization_str_mv | urn:organizationAcronym:unl |
| person_str_mv | Begiato, Rodolfo G. Custódio, Ana Luisa Gomes-Ruggiero, Márcia A. |
| publishDate | 2020 |
| reponame_str | Repositório Institucional da UNL |
| repository_id_str | urn:repositoryAcronym:run |
| service_str_mv | urn:repositoryAcronym:run |
| spelling | engenThis work concerns the numerical solution of high-dimensional systems of nonlinear equations, when derivatives are not available for use, but assuming that all functions defining the problem are continuously differentiable. A hybrid approach is taken, based on a derivative-free iterative method, organized in two phases. The first phase is defined by derivative-free versions of a fixed-point method that employs spectral parameters to define the steplength along the residual direction. The second phase consists on a matrix-free inexact Newton method that employs the Generalized Minimal Residual algorithm to solve the linear system that computes the search direction. This second phase will only take place if the first one fails to find a better point after a predefined number of reductions in the step size. In all stages, the criterion to accept a new point considers a nonmonotone decrease condition upon a merit function. Convergence results are established and the numerical performance is assessed through experiments in a set of problems collected from the literature. Both the theoretical and the experimental analysis support the feasibility of the proposed hybrid strategy.application/pdfenA global hybrid derivative-free method for high-dimensional systems of nonlinear equationsBegiato, Rodolfo G.Custódio, Ana LuisaGomes-Ruggiero, Márcia A.DM - Departamento de MatemáticaCMA - Centro de Matemática e AplicaçõesSpringer Science Business MediaHostingInstitutionOrganizationalRUNe-mailmailto:run@unl.ptrun@unl.ptISSNIsPartOf0926-6003URNIsPartOfPURE: 15483455URNIsPartOfPURE UUID: a74a8004-ab4d-442c-a127-c43a89d3e979URNIsPartOfScopus: 85074818447URNIsPartOfWOS: 000511695500004DOIIsPartOf10.1007/s10589-019-00149-y2021-04-26T22:55:03Z2020-01-012020-01-01T00:00:00ZHandlehttp://hdl.handle.net/10362/116219http://purl.org/coar/access_right/c_abf2open accessDerivative-free optimization methodsInexact NewtonNonlinear systems of equationsNonmonotone line searchSpectral residualControl and OptimizationComputational MathematicsApplied Mathematics764216 bytesliteraturehttp://purl.org/coar/resource_type/c_6501journal articlehttp://purl.org/coar/access_right/c_abf2application/pdffulltexthttps://run.unl.pt/bitstreams/fe0a0042-aec0-4ab1-9b3e-aa2f610538cf/download |
| spellingShingle | A global hybrid derivative-free method for high-dimensional systems of nonlinear equations Begiato, Rodolfo G. Derivative-free optimization methods Inexact Newton Nonlinear systems of equations Nonmonotone line search Spectral residual Control and Optimization Computational Mathematics Applied Mathematics |
| status | SINGLETON |
| subject.fl_str_mv | Derivative-free optimization methods Inexact Newton Nonlinear systems of equations Nonmonotone line search Spectral residual Control and Optimization Computational Mathematics Applied Mathematics |
| title | A global hybrid derivative-free method for high-dimensional systems of nonlinear equations |
| title_full | A global hybrid derivative-free method for high-dimensional systems of nonlinear equations |
| title_fullStr | A global hybrid derivative-free method for high-dimensional systems of nonlinear equations |
| title_full_unstemmed | A global hybrid derivative-free method for high-dimensional systems of nonlinear equations |
| title_short | A global hybrid derivative-free method for high-dimensional systems of nonlinear equations |
| title_sort | A global hybrid derivative-free method for high-dimensional systems of nonlinear equations |
| topic | Derivative-free optimization methods Inexact Newton Nonlinear systems of equations Nonmonotone line search Spectral residual Control and Optimization Computational Mathematics Applied Mathematics |
| topic_facet | Derivative-free optimization methods Inexact Newton Nonlinear systems of equations Nonmonotone line search Spectral residual Control and Optimization Computational Mathematics Applied Mathematics |
| url | http://hdl.handle.net/10362/116219 |
| visible | 1 |