{"id":"https://openalex.org/W2139081976","doi":"https://doi.org/10.1080/10556780500099944","title":"A globalization strategy for the multigrid solution of elliptic optimal control problems","display_name":"A globalization strategy for the multigrid solution of elliptic optimal control problems","publication_year":2006,"publication_date":"2006-01-17","ids":{"openalex":"https://openalex.org/W2139081976","doi":"https://doi.org/10.1080/10556780500099944","mag":"2139081976"},"language":"en","primary_location":{"id":"doi:10.1080/10556780500099944","is_oa":false,"landing_page_url":"https://doi.org/10.1080/10556780500099944","pdf_url":null,"source":{"id":"https://openalex.org/S103047102","display_name":"Optimization methods & software","issn_l":"1026-7670","issn":["1026-7670","1029-4937","1055-6788"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Optimization Methods and Software","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5027648225","display_name":"Alfio Borz\u0131\u0300","orcid":"https://orcid.org/0000-0002-8050-1336"},"institutions":[{"id":"https://openalex.org/I15766117","display_name":"University of Graz","ror":"https://ror.org/01faaaf77","country_code":"AT","type":"education","lineage":["https://openalex.org/I15766117"]}],"countries":["AT"],"is_corresponding":true,"raw_author_name":"A. Borz\u00ec","raw_affiliation_strings":["Institut f\u00fcr Mathematik und Wissenschaftliches Rechnen, Karl-Franzens-Universit\u00e4t Graz , Heinrich str. 36, A-8010, Graz,  Austria","Institut f\u00fcr Mathematik und Wissenschaftliches Rechnen, Karl-Franzens-Universit\u00e4t Graz , Heinrich str. 36, A-8010, Graz, Austria"],"affiliations":[{"raw_affiliation_string":"Institut f\u00fcr Mathematik und Wissenschaftliches Rechnen, Karl-Franzens-Universit\u00e4t Graz , Heinrich str. 36, A-8010, Graz,  Austria","institution_ids":["https://openalex.org/I15766117"]},{"raw_affiliation_string":"Institut f\u00fcr Mathematik und Wissenschaftliches Rechnen, Karl-Franzens-Universit\u00e4t Graz , Heinrich str. 36, A-8010, Graz, Austria","institution_ids":["https://openalex.org/I15766117"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5074607617","display_name":"Karl Kunisch","orcid":"https://orcid.org/0000-0003-1113-7355"},"institutions":[{"id":"https://openalex.org/I15766117","display_name":"University of Graz","ror":"https://ror.org/01faaaf77","country_code":"AT","type":"education","lineage":["https://openalex.org/I15766117"]}],"countries":["AT"],"is_corresponding":false,"raw_author_name":"K. Kunisch","raw_affiliation_strings":["Institut f\u00fcr Mathematik und Wissenschaftliches Rechnen, Karl-Franzens-Universit\u00e4t Graz , Heinrich str. 36, A-8010, Graz,  Austria","Institut f\u00fcr Mathematik und Wissenschaftliches Rechnen, Karl-Franzens-Universit\u00e4t Graz , Heinrich str. 36, A-8010, Graz, Austria"],"affiliations":[{"raw_affiliation_string":"Institut f\u00fcr Mathematik und Wissenschaftliches Rechnen, Karl-Franzens-Universit\u00e4t Graz , Heinrich str. 36, A-8010, Graz,  Austria","institution_ids":["https://openalex.org/I15766117"]},{"raw_affiliation_string":"Institut f\u00fcr Mathematik und Wissenschaftliches Rechnen, Karl-Franzens-Universit\u00e4t Graz , Heinrich str. 36, A-8010, Graz, Austria","institution_ids":["https://openalex.org/I15766117"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5027648225"],"corresponding_institution_ids":["https://openalex.org/I15766117"],"apc_list":null,"apc_paid":null,"fwci":2.8797,"has_fulltext":false,"cited_by_count":17,"citation_normalized_percentile":{"value":0.90448955,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"21","issue":"3","first_page":"445","last_page":"459"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10173","display_name":"Computational Fluid Dynamics and Aerodynamics","score":0.9987999796867371,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9979000091552734,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/multigrid-method","display_name":"Multigrid method","score":0.942977786064148},{"id":"https://openalex.org/keywords/hessian-matrix","display_name":"Hessian matrix","score":0.8105554580688477},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.6828916072845459},{"id":"https://openalex.org/keywords/curvature","display_name":"Curvature","score":0.6513881683349609},{"id":"https://openalex.org/keywords/descent","display_name":"Descent (aeronautics)","score":0.5635379552841187},{"id":"https://openalex.org/keywords/saddle-point","display_name":"Saddle point","score":0.5505328178405762},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5396004915237427},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5111425518989563},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.47816166281700134},{"id":"https://openalex.org/keywords/optimal-control","display_name":"Optimal control","score":0.43763408064842224},{"id":"https://openalex.org/keywords/maxima-and-minima","display_name":"Maxima and minima","score":0.41372787952423096},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.34849053621292114},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3272457420825958},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.17605221271514893},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.15691658854484558},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.1488487720489502}],"concepts":[{"id":"https://openalex.org/C137119250","wikidata":"https://www.wikidata.org/wiki/Q1413101","display_name":"Multigrid method","level":3,"score":0.942977786064148},{"id":"https://openalex.org/C203616005","wikidata":"https://www.wikidata.org/wiki/Q620495","display_name":"Hessian matrix","level":2,"score":0.8105554580688477},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.6828916072845459},{"id":"https://openalex.org/C195065555","wikidata":"https://www.wikidata.org/wiki/Q214881","display_name":"Curvature","level":2,"score":0.6513881683349609},{"id":"https://openalex.org/C2776637919","wikidata":"https://www.wikidata.org/wiki/Q624380","display_name":"Descent (aeronautics)","level":2,"score":0.5635379552841187},{"id":"https://openalex.org/C2681867","wikidata":"https://www.wikidata.org/wiki/Q690935","display_name":"Saddle point","level":2,"score":0.5505328178405762},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5396004915237427},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5111425518989563},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.47816166281700134},{"id":"https://openalex.org/C91575142","wikidata":"https://www.wikidata.org/wiki/Q1971426","display_name":"Optimal control","level":2,"score":0.43763408064842224},{"id":"https://openalex.org/C186633575","wikidata":"https://www.wikidata.org/wiki/Q845060","display_name":"Maxima and minima","level":2,"score":0.41372787952423096},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.34849053621292114},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3272457420825958},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.17605221271514893},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.15691658854484558},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.1488487720489502},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C153294291","wikidata":"https://www.wikidata.org/wiki/Q25261","display_name":"Meteorology","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1080/10556780500099944","is_oa":false,"landing_page_url":"https://doi.org/10.1080/10556780500099944","pdf_url":null,"source":{"id":"https://openalex.org/S103047102","display_name":"Optimization methods & software","issn_l":"1026-7670","issn":["1026-7670","1029-4937","1055-6788"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Optimization Methods and Software","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":18,"referenced_works":["https://openalex.org/W1497750339","https://openalex.org/W1497771620","https://openalex.org/W1976792725","https://openalex.org/W1984648213","https://openalex.org/W1992896645","https://openalex.org/W2013737143","https://openalex.org/W2022977680","https://openalex.org/W2038253697","https://openalex.org/W2043430160","https://openalex.org/W2062226392","https://openalex.org/W2065000345","https://openalex.org/W2085160061","https://openalex.org/W2127981460","https://openalex.org/W2151317657","https://openalex.org/W2480154215","https://openalex.org/W3022136271","https://openalex.org/W4230055019","https://openalex.org/W4298228534"],"related_works":["https://openalex.org/W2153649672","https://openalex.org/W1996762907","https://openalex.org/W131971937","https://openalex.org/W1989888202","https://openalex.org/W2095858157","https://openalex.org/W1557737441","https://openalex.org/W2324860879","https://openalex.org/W2752635268","https://openalex.org/W3100522340","https://openalex.org/W2021599769"],"abstract_inverted_index":{"A":[0],"globalization":[1,38],"strategy":[2],"for":[3,15],"multigrid":[4,30,60],"schemes":[5],"solving":[6],"optimal":[7],"control":[8],"problems":[9],"is":[10,46,56],"presented.":[11],"This":[12],"approach":[13],"searches":[14],"possible":[16],"negative":[17,33,44],"eigenvalues":[18,34],"of":[19,28,43],"the":[20,25,29,41,59,74],"reduced":[21],"Hessian":[22],"considered":[23],"at":[24],"coarsest":[26],"grid":[27],"process.":[31],"If":[32],"are":[35,68],"detected,":[36],"a":[37,64],"step":[39,62],"in":[40],"direction":[42],"curvature":[45],"performed":[47],"to":[48,70],"escape":[49],"undesired":[50],"maxima":[51],"or":[52],"saddle":[53],"points.":[54],"It":[55],"shown":[57],"that":[58],"solution":[61],"provides":[63],"descent":[65],"update.":[66],"Examples":[67],"given":[69],"illustrate":[71],"and":[72],"validate":[73],"present":[75],"approach.":[76]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":3},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}