{"id":"https://openalex.org/W2787938015","doi":"https://doi.org/10.1007/s10957-018-1408-0","title":"Metric and Geometric Relaxations of Self-Contracted Curves","display_name":"Metric and Geometric Relaxations of Self-Contracted Curves","publication_year":2018,"publication_date":"2018-10-13","ids":{"openalex":"https://openalex.org/W2787938015","doi":"https://doi.org/10.1007/s10957-018-1408-0","mag":"2787938015"},"language":"en","primary_location":{"id":"doi:10.1007/s10957-018-1408-0","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10957-018-1408-0","pdf_url":null,"source":{"id":"https://openalex.org/S52430896","display_name":"Journal of Optimization Theory and Applications","issn_l":"0022-3239","issn":["0022-3239","1573-2878"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Optimization Theory and Applications","raw_type":"journal-article"},"type":"preprint","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1802.09637","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5052741067","display_name":"Aris Daniilidis","orcid":"https://orcid.org/0000-0003-4837-694X"},"institutions":[{"id":"https://openalex.org/I69737025","display_name":"University of Chile","ror":"https://ror.org/047gc3g35","country_code":"CL","type":"education","lineage":["https://openalex.org/I69737025"]}],"countries":["CL"],"is_corresponding":true,"raw_author_name":"Aris Daniilidis","raw_affiliation_strings":["DIM\u2013CMM, UMI CNRS 2807, Universidad de Chile, Santiago, Chile"],"affiliations":[{"raw_affiliation_string":"DIM\u2013CMM, UMI CNRS 2807, Universidad de Chile, Santiago, Chile","institution_ids":["https://openalex.org/I69737025"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5107311427","display_name":"Robert Deville","orcid":"https://orcid.org/0000-0002-8859-9526"},"institutions":[{"id":"https://openalex.org/I15057530","display_name":"Universit\u00e9 de Bordeaux","ror":"https://ror.org/057qpr032","country_code":"FR","type":"education","lineage":["https://openalex.org/I15057530"]},{"id":"https://openalex.org/I4210166017","display_name":"Institut de Math\u00e9matiques de Bordeaux","ror":"https://ror.org/05m3r1b84","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I1326498283","https://openalex.org/I15057530","https://openalex.org/I4210141950","https://openalex.org/I4210160189","https://openalex.org/I4210166017"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Robert Deville","raw_affiliation_strings":["Laboratoire Bordelais d\u2019Analyse et Geom\u00e9trie, Institut de Math\u00e9matiques de Bordeaux, Universit\u00e9 de Bordeaux 1, Bordeaux, France"],"affiliations":[{"raw_affiliation_string":"Laboratoire Bordelais d\u2019Analyse et Geom\u00e9trie, Institut de Math\u00e9matiques de Bordeaux, Universit\u00e9 de Bordeaux 1, Bordeaux, France","institution_ids":["https://openalex.org/I4210166017","https://openalex.org/I15057530"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5103559605","display_name":"Estibalitz Durand Cartagena","orcid":null},"institutions":[{"id":"https://openalex.org/I178450904","display_name":"Universidad Nacional de Educaci\u00f3n a Distancia","ror":"https://ror.org/02msb5n36","country_code":"ES","type":"education","lineage":["https://openalex.org/I178450904"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"Estibalitz Durand-Cartagena","raw_affiliation_strings":["Departamento de Matem\u00e1tica Aplicada, ETSI Industriales, UNED, Madrid, Spain"],"affiliations":[{"raw_affiliation_string":"Departamento de Matem\u00e1tica Aplicada, ETSI Industriales, UNED, Madrid, Spain","institution_ids":["https://openalex.org/I178450904"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5052741067"],"corresponding_institution_ids":["https://openalex.org/I69737025"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.04157107,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"182","issue":"1","first_page":"81","last_page":"109"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10229","display_name":"Geometric Analysis and Curvature Flows","score":0.987500011920929,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/T10229","display_name":"Geometric Analysis and Curvature Flows","score":0.987500011920929,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9704999923706055,"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/T13267","display_name":"Advanced Theoretical and Applied Studies in Material Sciences and Geometry","score":0.9610000252723694,"subfield":{"id":"https://openalex.org/subfields/2204","display_name":"Biomedical 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/lambda","display_name":"Lambda","score":0.8216188549995422},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.735901951789856},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7147425413131714},{"id":"https://openalex.org/keywords/metric-space","display_name":"Metric space","score":0.5344103574752808},{"id":"https://openalex.org/keywords/euclidean-space","display_name":"Euclidean space","score":0.5157725811004639},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5098263621330261},{"id":"https://openalex.org/keywords/cone","display_name":"Cone (formal languages)","score":0.496175616979599},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.48029085993766785},{"id":"https://openalex.org/keywords/euclidean-geometry","display_name":"Euclidean geometry","score":0.46592116355895996},{"id":"https://openalex.org/keywords/metric","display_name":"Metric (unit)","score":0.4376709461212158},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3446790874004364},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.3079160451889038},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.13599777221679688},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.07068166136741638},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.05811959505081177}],"concepts":[{"id":"https://openalex.org/C2778113609","wikidata":"https://www.wikidata.org/wiki/Q10897","display_name":"Lambda","level":2,"score":0.8216188549995422},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.735901951789856},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7147425413131714},{"id":"https://openalex.org/C198043062","wikidata":"https://www.wikidata.org/wiki/Q180953","display_name":"Metric space","level":2,"score":0.5344103574752808},{"id":"https://openalex.org/C186450821","wikidata":"https://www.wikidata.org/wiki/Q17295","display_name":"Euclidean space","level":2,"score":0.5157725811004639},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5098263621330261},{"id":"https://openalex.org/C30014739","wikidata":"https://www.wikidata.org/wiki/Q5159445","display_name":"Cone (formal languages)","level":2,"score":0.496175616979599},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.48029085993766785},{"id":"https://openalex.org/C129782007","wikidata":"https://www.wikidata.org/wiki/Q162886","display_name":"Euclidean geometry","level":2,"score":0.46592116355895996},{"id":"https://openalex.org/C176217482","wikidata":"https://www.wikidata.org/wiki/Q860554","display_name":"Metric (unit)","level":2,"score":0.4376709461212158},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3446790874004364},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.3079160451889038},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.13599777221679688},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.07068166136741638},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.05811959505081177},{"id":"https://openalex.org/C120665830","wikidata":"https://www.wikidata.org/wiki/Q14620","display_name":"Optics","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/C21547014","wikidata":"https://www.wikidata.org/wiki/Q1423657","display_name":"Operations management","level":1,"score":0.0},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0}],"mesh":[],"locations_count":9,"locations":[{"id":"doi:10.1007/s10957-018-1408-0","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10957-018-1408-0","pdf_url":null,"source":{"id":"https://openalex.org/S52430896","display_name":"Journal of Optimization Theory and Applications","issn_l":"0022-3239","issn":["0022-3239","1573-2878"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Optimization Theory and Applications","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1802.09637","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1802.09637","pdf_url":"https://arxiv.org/pdf/1802.09637","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"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"},{"id":"mag:2787938015","is_oa":true,"landing_page_url":"http://arxiv.org/pdf/1802.09637.pdf","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},{"id":"pmh:oai:HAL:hal-02478402v1","is_oa":false,"landing_page_url":"https://hal.science/hal-02478402","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Journal of Optimization Theory and Applications, 2019, 182 (1), pp.81-109. ⟨10.1007/s10957-018-1408-0⟩","raw_type":"Journal articles"},{"id":"pmh:oai:RePEc:spr:joptap:v:182:y:2019:i:1:d:10.1007_s10957-018-1408-0","is_oa":false,"landing_page_url":"http://link.springer.com/10.1007/s10957-018-1408-0","pdf_url":null,"source":{"id":"https://openalex.org/S4306401271","display_name":"RePEc: Research Papers in Economics","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I77793887","host_organization_name":"Federal Reserve Bank of St. Louis","host_organization_lineage":["https://openalex.org/I77793887"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"},{"id":"pmh:oai:oskar-bordeaux.fr:20.500.12278/192539","is_oa":false,"landing_page_url":"https://oskar-bordeaux.fr/handle/20.500.12278/192539","pdf_url":null,"source":{"id":"https://openalex.org/S4306402569","display_name":"Oskar-Bordeaux (Universite de Bordeaux)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Article de revue"},{"id":"pmh:oai:oskar-bordeaux.fr:20.500.12278/9013","is_oa":false,"landing_page_url":"https://oskar-bordeaux.fr/handle/20.500.12278/9013","pdf_url":null,"source":{"id":"https://openalex.org/S4306402569","display_name":"Oskar-Bordeaux (Universite de Bordeaux)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Article de revue"},{"id":"pmh:oai:repositorio.uchile.cl:2250/171345","is_oa":true,"landing_page_url":"https://repositorio.uchile.cl/handle/2250/171345","pdf_url":null,"source":{"id":"https://openalex.org/S4306481413","display_name":"Universidad de Chile","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Journal of Optimization Theory and Applications","raw_type":"Art\u00edculo de revista"},{"id":"doi:10.48550/arxiv.1802.09637","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1802.09637","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1802.09637","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1802.09637","pdf_url":"https://arxiv.org/pdf/1802.09637","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"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"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":11,"referenced_works":["https://openalex.org/W1966445912","https://openalex.org/W1984205401","https://openalex.org/W2001561278","https://openalex.org/W2038045421","https://openalex.org/W2136028432","https://openalex.org/W2340467693","https://openalex.org/W2591625315","https://openalex.org/W2602919751","https://openalex.org/W2963892210","https://openalex.org/W4249513058","https://openalex.org/W6601714753"],"related_works":["https://openalex.org/W3099174010","https://openalex.org/W2314212732","https://openalex.org/W3103265030","https://openalex.org/W2950044146","https://openalex.org/W2734336346","https://openalex.org/W2788810596","https://openalex.org/W3103997687","https://openalex.org/W3040834715","https://openalex.org/W1626249095","https://openalex.org/W2894905015","https://openalex.org/W2973422078","https://openalex.org/W2969291076","https://openalex.org/W1924327771","https://openalex.org/W3206330529","https://openalex.org/W2950925562","https://openalex.org/W3139156389","https://openalex.org/W2062223381","https://openalex.org/W1993364643","https://openalex.org/W2743895475","https://openalex.org/W2913291429"],"abstract_inverted_index":null,"counts_by_year":[],"updated_date":"2026-03-27T05:58:40.876381","created_date":"2025-10-10T00:00:00"}