{"id":"https://openalex.org/W2070289182","doi":"https://doi.org/10.1137/040611598","title":"Path-following Methods for a Class of Constrained Minimization Problems in Function Space","display_name":"Path-following Methods for a Class of Constrained Minimization Problems in Function Space","publication_year":2006,"publication_date":"2006-01-01","ids":{"openalex":"https://openalex.org/W2070289182","doi":"https://doi.org/10.1137/040611598","mag":"2070289182"},"language":"en","primary_location":{"id":"doi:10.1137/040611598","is_oa":false,"landing_page_url":"https://doi.org/10.1137/040611598","pdf_url":null,"source":{"id":"https://openalex.org/S928796702","display_name":"SIAM Journal on Optimization","issn_l":"1052-6234","issn":["1052-6234","1095-7189"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Optimization","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://figshare.com/articles/journal_contribution/Path-following_methods_for_a_class_of_constrained_minimization_problems_in_function_space/23336603","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5062202097","display_name":"Michael Hinterm\u00fcller","orcid":"https://orcid.org/0000-0001-9471-2479"},"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"]},{"id":"https://openalex.org/I74775410","display_name":"Rice University","ror":"https://ror.org/008zs3103","country_code":"US","type":"education","lineage":["https://openalex.org/I74775410"]}],"countries":["AT","US"],"is_corresponding":false,"raw_author_name":"Michael Hinterm\u00fcller","raw_affiliation_strings":["Institute of Mathematics and Scientific Computing, University of Graz, Graz, Austria","Department of Computational and Applied Mathematics, Rice University, Houston, TX"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Mathematics and Scientific Computing, University of Graz, Graz, Austria","institution_ids":["https://openalex.org/I15766117"]},{"raw_affiliation_string":"Department of Computational and Applied Mathematics, Rice University, Houston, TX","institution_ids":["https://openalex.org/I74775410"]}]},{"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":"Karl Kunisch","raw_affiliation_strings":["Institute of Mathematics and Scientific Computing, University of Graz, Graz, Austria"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Mathematics and Scientific Computing, University of Graz, Graz, Austria","institution_ids":["https://openalex.org/I15766117"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":13.6013,"has_fulltext":false,"cited_by_count":108,"citation_normalized_percentile":{"value":0.99302615,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"17","issue":"1","first_page":"159","last_page":"187"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10545","display_name":"Optimization and Variational Analysis","score":0.9991999864578247,"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"}},{"id":"https://openalex.org/T10791","display_name":"Advanced Control Systems Optimization","score":0.9955000281333923,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.822782039642334},{"id":"https://openalex.org/keywords/convexity","display_name":"Convexity","score":0.7262095212936401},{"id":"https://openalex.org/keywords/monotonic-function","display_name":"Monotonic function","score":0.7107927799224854},{"id":"https://openalex.org/keywords/path","display_name":"Path (computing)","score":0.6351417899131775},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.6234104633331299},{"id":"https://openalex.org/keywords/regularization","display_name":"Regularization (linguistics)","score":0.5856754183769226},{"id":"https://openalex.org/keywords/differentiable-function","display_name":"Differentiable function","score":0.49123185873031616},{"id":"https://openalex.org/keywords/minification","display_name":"Minification","score":0.48808515071868896},{"id":"https://openalex.org/keywords/dual","display_name":"Dual (grammatical number)","score":0.45772111415863037},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.13228699564933777},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.12442606687545776}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.822782039642334},{"id":"https://openalex.org/C72134830","wikidata":"https://www.wikidata.org/wiki/Q5166524","display_name":"Convexity","level":2,"score":0.7262095212936401},{"id":"https://openalex.org/C72169020","wikidata":"https://www.wikidata.org/wiki/Q194404","display_name":"Monotonic function","level":2,"score":0.7107927799224854},{"id":"https://openalex.org/C2777735758","wikidata":"https://www.wikidata.org/wiki/Q817765","display_name":"Path (computing)","level":2,"score":0.6351417899131775},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.6234104633331299},{"id":"https://openalex.org/C2776135515","wikidata":"https://www.wikidata.org/wiki/Q17143721","display_name":"Regularization (linguistics)","level":2,"score":0.5856754183769226},{"id":"https://openalex.org/C202615002","wikidata":"https://www.wikidata.org/wiki/Q783507","display_name":"Differentiable function","level":2,"score":0.49123185873031616},{"id":"https://openalex.org/C147764199","wikidata":"https://www.wikidata.org/wiki/Q6865248","display_name":"Minification","level":2,"score":0.48808515071868896},{"id":"https://openalex.org/C2780980858","wikidata":"https://www.wikidata.org/wiki/Q110022","display_name":"Dual (grammatical number)","level":2,"score":0.45772111415863037},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.13228699564933777},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.12442606687545776},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C142362112","wikidata":"https://www.wikidata.org/wiki/Q735","display_name":"Art","level":0,"score":0.0},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C124952713","wikidata":"https://www.wikidata.org/wiki/Q8242","display_name":"Literature","level":1,"score":0.0},{"id":"https://openalex.org/C106159729","wikidata":"https://www.wikidata.org/wiki/Q2294553","display_name":"Financial economics","level":1,"score":0.0}],"mesh":[],"locations_count":8,"locations":[{"id":"doi:10.1137/040611598","is_oa":false,"landing_page_url":"https://doi.org/10.1137/040611598","pdf_url":null,"source":{"id":"https://openalex.org/S928796702","display_name":"SIAM Journal on Optimization","issn_l":"1052-6234","issn":["1052-6234","1095-7189"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Optimization","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.2.1363","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.2.1363","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.caam.rice.edu/caam/trs/2004/TR04-11.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.210.2935","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.210.2935","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.ricam.oeaw.ac.at/publications/reports/04/rep04-07.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.909.6526","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.909.6526","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.ricam.oeaw.ac.at/files/reports/04/rep04-17.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.921.2187","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.921.2187","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"https://www.ricam.oeaw.ac.at/files/reports/04/rep04-07.pdf","raw_type":"text"},{"id":"pmh:oai:figshare.com:article/23336603","is_oa":true,"landing_page_url":"https://figshare.com/articles/journal_contribution/Path-following_methods_for_a_class_of_constrained_minimization_problems_in_function_space/23336603","pdf_url":null,"source":{"id":"https://openalex.org/S4377196282","display_name":"Figshare","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210132348","host_organization_name":"Figshare (United Kingdom)","host_organization_lineage":["https://openalex.org/I4210132348"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Text"},{"id":"pmh:oai:scholarship.rice.edu:1911/102023","is_oa":false,"landing_page_url":"http://hdl.handle.net/1911/102023","pdf_url":null,"source":{"id":"https://openalex.org/S4306401268","display_name":"Rice Digital Scholarship Archive (Rice University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I74775410","host_organization_name":"Rice University","host_organization_lineage":["https://openalex.org/I74775410"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Technical report"},{"id":"pmh:oai:unipub.uni-graz.at:133143","is_oa":false,"landing_page_url":"http://resolver.obvsg.at/urn:nbn:at:at-ubg:3-968","pdf_url":null,"source":{"id":"https://openalex.org/S4306400359","display_name":"Unipub UB Graz (Universit\u00e4t Graz)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I15766117","host_organization_name":"University of Graz","host_organization_lineage":["https://openalex.org/I15766117"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Text"}],"best_oa_location":{"id":"pmh:oai:figshare.com:article/23336603","is_oa":true,"landing_page_url":"https://figshare.com/articles/journal_contribution/Path-following_methods_for_a_class_of_constrained_minimization_problems_in_function_space/23336603","pdf_url":null,"source":{"id":"https://openalex.org/S4377196282","display_name":"Figshare","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210132348","host_organization_name":"Figshare (United Kingdom)","host_organization_lineage":["https://openalex.org/I4210132348"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Text"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":22,"referenced_works":["https://openalex.org/W25733641","https://openalex.org/W1492326914","https://openalex.org/W1495442750","https://openalex.org/W1509805685","https://openalex.org/W1518039036","https://openalex.org/W1976619285","https://openalex.org/W2014746566","https://openalex.org/W2022088322","https://openalex.org/W2026365342","https://openalex.org/W2037396431","https://openalex.org/W2063318629","https://openalex.org/W2069671092","https://openalex.org/W2070584352","https://openalex.org/W2075205943","https://openalex.org/W2121005322","https://openalex.org/W2135557790","https://openalex.org/W2142124856","https://openalex.org/W2158258156","https://openalex.org/W2482580142","https://openalex.org/W2798766386","https://openalex.org/W4236752279","https://openalex.org/W4254106911"],"related_works":["https://openalex.org/W4389849086","https://openalex.org/W4281957576","https://openalex.org/W2164621095","https://openalex.org/W1545461878","https://openalex.org/W2952133296","https://openalex.org/W3130449832","https://openalex.org/W3120050151","https://openalex.org/W2096962213","https://openalex.org/W4254682493","https://openalex.org/W1996226968"],"abstract_inverted_index":{"Path-following":[0],"methods":[1],"for":[2],"primal-dual":[3,16,29],"active":[4],"set":[5],"strategies":[6,44],"requiring":[7],"a":[8,15],"regularization":[9],"parameter":[10],"are":[11,22,33,40,45],"introduced.":[12],"Existence":[13],"of":[14,27,54],"path":[17,30],"and":[18,25,37,47],"its":[19],"differentiability":[20],"properties":[21],"analyzed.":[23],"Monotonicity":[24],"convexity":[26],"the":[28],"value":[31],"function":[32],"investigated.":[34],"Both":[35],"feasible":[36],"infeasible":[38],"approximations":[39],"considered.":[41],"Numerical":[42],"path-following":[43],"developed":[46],"their":[48],"efficiency":[49],"is":[50],"demonstrated":[51],"by":[52],"means":[53],"examples.":[55]},"counts_by_year":[{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":6},{"year":2021,"cited_by_count":6},{"year":2020,"cited_by_count":5},{"year":2019,"cited_by_count":5},{"year":2018,"cited_by_count":6},{"year":2017,"cited_by_count":4},{"year":2016,"cited_by_count":8},{"year":2015,"cited_by_count":5},{"year":2014,"cited_by_count":4},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":3}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}