{"id":"https://openalex.org/W4401730575","doi":"https://doi.org/10.1007/s10957-024-02488-1","title":"Stochastic Augmented Lagrangian Method in Riemannian Shape Manifolds","display_name":"Stochastic Augmented Lagrangian Method in Riemannian Shape Manifolds","publication_year":2024,"publication_date":"2024-08-21","ids":{"openalex":"https://openalex.org/W4401730575","doi":"https://doi.org/10.1007/s10957-024-02488-1"},"language":"en","primary_location":{"id":"doi:10.1007/s10957-024-02488-1","is_oa":true,"landing_page_url":"http://dx.doi.org/10.1007/s10957-024-02488-1","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10957-024-02488-1.pdf","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Optimization Theory and Applications","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s10957-024-02488-1.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5033054577","display_name":"Caroline Geiersbach","orcid":"https://orcid.org/0000-0002-6518-7756"},"institutions":[{"id":"https://openalex.org/I4210092021","display_name":"Weierstrass Institute for Applied Analysis and Stochastics","ror":"https://ror.org/00h1x4t21","country_code":"DE","type":"facility","lineage":["https://openalex.org/I315704651","https://openalex.org/I4210092021"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Caroline Geiersbach","raw_affiliation_strings":["Weierstrass Institute, Mohrenstra\u00dfe 39, 10117, Berlin, Germany"],"affiliations":[{"raw_affiliation_string":"Weierstrass Institute, Mohrenstra\u00dfe 39, 10117, Berlin, Germany","institution_ids":["https://openalex.org/I4210092021"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5008089792","display_name":"Tim Suchan","orcid":"https://orcid.org/0000-0001-5847-5613"},"institutions":[{"id":"https://openalex.org/I190134885","display_name":"Helmut Schmidt University","ror":"https://ror.org/04e8jbs38","country_code":"DE","type":"education","lineage":["https://openalex.org/I190134885"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Tim Suchan","raw_affiliation_strings":["Faculty of Mechanical and Civil Engineering, Helmut Schmidt University/University of the Federal Armed Forces Hamburg, Holstenhofweg 85, 22043, Hamburg, Germany"],"affiliations":[{"raw_affiliation_string":"Faculty of Mechanical and Civil Engineering, Helmut Schmidt University/University of the Federal Armed Forces Hamburg, Holstenhofweg 85, 22043, Hamburg, Germany","institution_ids":["https://openalex.org/I190134885"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5041753823","display_name":"Kathrin Welker","orcid":"https://orcid.org/0000-0002-6673-9436"},"institutions":[{"id":"https://openalex.org/I61893789","display_name":"TU Bergakademie Freiberg","ror":"https://ror.org/031vc2293","country_code":"DE","type":"education","lineage":["https://openalex.org/I61893789"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Kathrin Welker","raw_affiliation_strings":["Faculty of Mathematics and Computer Science, TU Bergakademie Freiberg, Akademiestr.\u00a06, 09599, Freiberg, Germany"],"affiliations":[{"raw_affiliation_string":"Faculty of Mathematics and Computer Science, TU Bergakademie Freiberg, Akademiestr.\u00a06, 09599, Freiberg, Germany","institution_ids":["https://openalex.org/I61893789"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5033054577"],"corresponding_institution_ids":["https://openalex.org/I4210092021"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":{"value":2390,"currency":"EUR","value_usd":2990},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.14434134,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"203","issue":"1","first_page":"165","last_page":"195"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10719","display_name":"3D Shape Modeling and Analysis","score":0.9993000030517578,"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/T10719","display_name":"3D Shape Modeling and Analysis","score":0.9993000030517578,"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/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9977999925613403,"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/T10481","display_name":"Computer Graphics and Visualization Techniques","score":0.9937999844551086,"subfield":{"id":"https://openalex.org/subfields/1704","display_name":"Computer Graphics and Computer-Aided Design"},"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/mathematics","display_name":"Mathematics","score":0.8353315591812134},{"id":"https://openalex.org/keywords/lagrangian","display_name":"Lagrangian","score":0.6857361793518066},{"id":"https://openalex.org/keywords/theory-of-computation","display_name":"Theory of computation","score":0.6757783889770508},{"id":"https://openalex.org/keywords/augmented-lagrangian-method","display_name":"Augmented Lagrangian method","score":0.6066693663597107},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4371907711029053},{"id":"https://openalex.org/keywords/riemannian-geometry","display_name":"Riemannian geometry","score":0.4327976703643799},{"id":"https://openalex.org/keywords/riemannian-manifold","display_name":"Riemannian manifold","score":0.4204620122909546},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.36781275272369385},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.2648911476135254},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.08902499079704285}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8353315591812134},{"id":"https://openalex.org/C53469067","wikidata":"https://www.wikidata.org/wiki/Q505735","display_name":"Lagrangian","level":2,"score":0.6857361793518066},{"id":"https://openalex.org/C24858836","wikidata":"https://www.wikidata.org/wiki/Q844718","display_name":"Theory of computation","level":2,"score":0.6757783889770508},{"id":"https://openalex.org/C150452318","wikidata":"https://www.wikidata.org/wiki/Q4820432","display_name":"Augmented Lagrangian method","level":2,"score":0.6066693663597107},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4371907711029053},{"id":"https://openalex.org/C181104567","wikidata":"https://www.wikidata.org/wiki/Q761383","display_name":"Riemannian geometry","level":2,"score":0.4327976703643799},{"id":"https://openalex.org/C2779593128","wikidata":"https://www.wikidata.org/wiki/Q632814","display_name":"Riemannian manifold","level":2,"score":0.4204620122909546},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.36781275272369385},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.2648911476135254},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.08902499079704285}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/s10957-024-02488-1","is_oa":true,"landing_page_url":"http://dx.doi.org/10.1007/s10957-024-02488-1","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10957-024-02488-1.pdf","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Optimization Theory and Applications","raw_type":"journal-article"},{"id":"pmh:oai:RePEc:spr:joptap:v:203:y:2024:i:1:d:10.1007_s10957-024-02488-1","is_oa":false,"landing_page_url":"http://link.springer.com/10.1007/s10957-024-02488-1","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"}],"best_oa_location":{"id":"doi:10.1007/s10957-024-02488-1","is_oa":true,"landing_page_url":"http://dx.doi.org/10.1007/s10957-024-02488-1","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10957-024-02488-1.pdf","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Optimization Theory and Applications","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2097767187","display_name":null,"funder_award_id":"WE 6629/1-1","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G3633743130","display_name":null,"funder_award_id":"SPP 1","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G6052429835","display_name":null,"funder_award_id":"(DFG)","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G6507445336","display_name":null,"funder_award_id":"SPP 1962","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G8330397625","display_name":null,"funder_award_id":"Funding","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G8928656450","display_name":null,"funder_award_id":"Projekt DEAL","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"}],"funders":[{"id":"https://openalex.org/F4320320300","display_name":"European Commission","ror":"https://ror.org/00k4n6c32"},{"id":"https://openalex.org/F4320320879","display_name":"Deutsche Forschungsgemeinschaft","ror":"https://ror.org/018mejw64"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4401730575.pdf","grobid_xml":"https://content.openalex.org/works/W4401730575.grobid-xml"},"referenced_works_count":55,"referenced_works":["https://openalex.org/W205960364","https://openalex.org/W310341204","https://openalex.org/W646582900","https://openalex.org/W1669104078","https://openalex.org/W1977272864","https://openalex.org/W1985415289","https://openalex.org/W2005681075","https://openalex.org/W2029463628","https://openalex.org/W2045881510","https://openalex.org/W2094997686","https://openalex.org/W2095444191","https://openalex.org/W2112311198","https://openalex.org/W2132630784","https://openalex.org/W2138674039","https://openalex.org/W2147191758","https://openalex.org/W2160971072","https://openalex.org/W2170382756","https://openalex.org/W2212370034","https://openalex.org/W2492283546","https://openalex.org/W2732075869","https://openalex.org/W2767229563","https://openalex.org/W2768686860","https://openalex.org/W2786622712","https://openalex.org/W2791183871","https://openalex.org/W2797479470","https://openalex.org/W2803862123","https://openalex.org/W2891420811","https://openalex.org/W2926858747","https://openalex.org/W2947854252","https://openalex.org/W2962812279","https://openalex.org/W2963067150","https://openalex.org/W2963350927","https://openalex.org/W2963470657","https://openalex.org/W2963704853","https://openalex.org/W3021986546","https://openalex.org/W3102317997","https://openalex.org/W3102383992","https://openalex.org/W3102552524","https://openalex.org/W3103296069","https://openalex.org/W3103831263","https://openalex.org/W3105995075","https://openalex.org/W3123321780","https://openalex.org/W3195280213","https://openalex.org/W3203464873","https://openalex.org/W4205293427","https://openalex.org/W4205755138","https://openalex.org/W4206302008","https://openalex.org/W4212889321","https://openalex.org/W4237284205","https://openalex.org/W4240092573","https://openalex.org/W4250800977","https://openalex.org/W4292070112","https://openalex.org/W4321782451","https://openalex.org/W4385435086","https://openalex.org/W6889056184"],"related_works":["https://openalex.org/W2315802443","https://openalex.org/W4394725424","https://openalex.org/W2082991255","https://openalex.org/W2767923834","https://openalex.org/W4392659495","https://openalex.org/W2029448249","https://openalex.org/W2289975471","https://openalex.org/W2376104286","https://openalex.org/W2082353735","https://openalex.org/W2999284236"],"abstract_inverted_index":{"Abstract":[0],"In":[1],"this":[2],"paper,":[3],"we":[4],"present":[5],"a":[6,22,39,60],"stochastic":[7,18,40],"augmented":[8],"Lagrangian":[9],"approach":[10,42],"on":[11,38],"(possibly":[12],"infinite-dimensional)":[13],"Riemannian":[14],"manifolds":[15],"to":[16,59],"solve":[17],"optimization":[19,62],"problems":[20],"with":[21,43,47,64],"finite":[23],"number":[24],"of":[25,32],"deterministic":[26],"constraints.":[27],"We":[28],"investigate":[29],"the":[30,33],"convergence":[31],"method,":[34],"which":[35],"is":[36,57],"based":[37],"approximation":[41],"random":[44],"stopping":[45],"combined":[46],"an":[48],"iterative":[49],"procedure":[50],"for":[51],"updating":[52],"Lagrange":[53],"multipliers.":[54],"The":[55],"algorithm":[56],"applied":[58],"multi-shape":[61],"problem":[63],"geometric":[65],"constraints":[66],"and":[67],"demonstrated":[68],"numerically.":[69]},"counts_by_year":[],"updated_date":"2026-03-21T08:13:44.787528","created_date":"2025-10-10T00:00:00"}
