{"id":"https://openalex.org/W2152429721","doi":"https://doi.org/10.1007/s10107-007-0115-7","title":"Augmented Lagrangians in semi-infinite programming","display_name":"Augmented Lagrangians in semi-infinite programming","publication_year":2007,"publication_date":"2007-05-02","ids":{"openalex":"https://openalex.org/W2152429721","doi":"https://doi.org/10.1007/s10107-007-0115-7","mag":"2152429721"},"language":"en","primary_location":{"id":"doi:10.1007/s10107-007-0115-7","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10107-007-0115-7","pdf_url":null,"source":{"id":"https://openalex.org/S193920097","display_name":"Mathematical Programming","issn_l":"0025-5610","issn":["0025-5610","1436-4646"],"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":"Mathematical Programming","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/A5062724317","display_name":"Jan-J. R\u00fcckmann","orcid":"https://orcid.org/0000-0002-9440-3294"},"institutions":[{"id":"https://openalex.org/I79619799","display_name":"University of Birmingham","ror":"https://ror.org/03angcq70","country_code":"GB","type":"education","lineage":["https://openalex.org/I79619799"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Jan-J. R\u00fcckmann","raw_affiliation_strings":["School of Mathematics, The University of Birmingham Edgbaston, Birmingham, B152TT, UK"],"affiliations":[{"raw_affiliation_string":"School of Mathematics, The University of Birmingham Edgbaston, Birmingham, B152TT, UK","institution_ids":["https://openalex.org/I79619799"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5025917676","display_name":"Alexander Shapiro","orcid":"https://orcid.org/0000-0002-4776-0053"},"institutions":[{"id":"https://openalex.org/I130701444","display_name":"Georgia Institute of Technology","ror":"https://ror.org/01zkghx44","country_code":"US","type":"education","lineage":["https://openalex.org/I130701444"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Alexander Shapiro","raw_affiliation_strings":["School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, GA, 30332-0205, USA"],"affiliations":[{"raw_affiliation_string":"School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, GA, 30332-0205, USA","institution_ids":["https://openalex.org/I130701444"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5025917676"],"corresponding_institution_ids":["https://openalex.org/I130701444"],"apc_list":{"value":2190,"currency":"EUR","value_usd":2890},"apc_paid":null,"fwci":0.3743,"has_fulltext":false,"cited_by_count":22,"citation_normalized_percentile":{"value":0.6683524,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":"116","issue":"1-2","first_page":"499","last_page":"512"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10545","display_name":"Optimization and Variational Analysis","score":0.9998000264167786,"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"}},"topics":[{"id":"https://openalex.org/T10545","display_name":"Optimization and Variational Analysis","score":0.9998000264167786,"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/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9980000257492065,"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/T11545","display_name":"Advanced Banach Space Theory","score":0.9835000038146973,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/augmented-lagrangian-method","display_name":"Augmented Lagrangian method","score":0.8397287130355835},{"id":"https://openalex.org/keywords/lagrange-multiplier","display_name":"Lagrange multiplier","score":0.8081716299057007},{"id":"https://openalex.org/keywords/lagrangian","display_name":"Lagrangian","score":0.7721056938171387},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.745614230632782},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.6302534341812134},{"id":"https://openalex.org/keywords/semi-infinite-programming","display_name":"Semi-infinite programming","score":0.6129125952720642},{"id":"https://openalex.org/keywords/inverse-problem-for-lagrangian-mechanics","display_name":"Inverse problem for Lagrangian mechanics","score":0.5955024361610413},{"id":"https://openalex.org/keywords/lagrangian-relaxation","display_name":"Lagrangian relaxation","score":0.5913317203521729},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5099748373031616},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4770236015319824},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.4456923305988312},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.3409044146537781},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.19734430313110352},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.17892718315124512},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.09902161359786987},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.0967288613319397}],"concepts":[{"id":"https://openalex.org/C150452318","wikidata":"https://www.wikidata.org/wiki/Q4820432","display_name":"Augmented Lagrangian method","level":2,"score":0.8397287130355835},{"id":"https://openalex.org/C73684929","wikidata":"https://www.wikidata.org/wiki/Q598870","display_name":"Lagrange multiplier","level":2,"score":0.8081716299057007},{"id":"https://openalex.org/C53469067","wikidata":"https://www.wikidata.org/wiki/Q505735","display_name":"Lagrangian","level":2,"score":0.7721056938171387},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.745614230632782},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.6302534341812134},{"id":"https://openalex.org/C2780394207","wikidata":"https://www.wikidata.org/wiki/Q7449304","display_name":"Semi-infinite programming","level":3,"score":0.6129125952720642},{"id":"https://openalex.org/C97491812","wikidata":"https://www.wikidata.org/wiki/Q6060414","display_name":"Inverse problem for Lagrangian mechanics","level":4,"score":0.5955024361610413},{"id":"https://openalex.org/C91765299","wikidata":"https://www.wikidata.org/wiki/Q3424292","display_name":"Lagrangian relaxation","level":2,"score":0.5913317203521729},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5099748373031616},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4770236015319824},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.4456923305988312},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3409044146537781},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.19734430313110352},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.17892718315124512},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.09902161359786987},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0967288613319397},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.0},{"id":"https://openalex.org/C181830111","wikidata":"https://www.wikidata.org/wiki/Q214850","display_name":"Gauge theory","level":2,"score":0.0},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C147247565","wikidata":"https://www.wikidata.org/wiki/Q5527635","display_name":"Gauge symmetry","level":3,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1007/s10107-007-0115-7","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10107-007-0115-7","pdf_url":null,"source":{"id":"https://openalex.org/S193920097","display_name":"Mathematical Programming","issn_l":"0025-5610","issn":["0025-5610","1436-4646"],"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":"Mathematical Programming","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.299.2652","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.299.2652","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www2.isye.gatech.edu/people/faculty/Alex_Shapiro/AL-SIP.pdf","raw_type":"text"},{"id":"pmh:oai:pure.atira.dk:openaire_cris_publications/f644240a-67fd-4bda-906a-196e2cdd0321","is_oa":false,"landing_page_url":"https://research.birmingham.ac.uk/en/publications/f644240a-67fd-4bda-906a-196e2cdd0321","pdf_url":null,"source":{"id":"https://openalex.org/S4306402634","display_name":"University of Birmingham Research Portal (University of Birmingham)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I79619799","host_organization_name":"University of Birmingham","host_organization_lineage":["https://openalex.org/I79619799"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Ruckmann, J-J & Shapiro, A 2009, 'Augmented Lagrangians in semi-infinite programming', Mathematical Programming, vol. 116, no. 1-2, pp. 499-512. https://doi.org/10.1007/s10107-007-0115-7","raw_type":"article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":19,"referenced_works":["https://openalex.org/W83112366","https://openalex.org/W580782046","https://openalex.org/W1556819741","https://openalex.org/W1577338488","https://openalex.org/W1601741115","https://openalex.org/W2037091587","https://openalex.org/W2057624533","https://openalex.org/W2062536941","https://openalex.org/W2075887074","https://openalex.org/W2107465205","https://openalex.org/W2114605231","https://openalex.org/W3012080241","https://openalex.org/W4214631981","https://openalex.org/W4232193086","https://openalex.org/W4249513058","https://openalex.org/W4285719527","https://openalex.org/W4293820388","https://openalex.org/W6603349842","https://openalex.org/W6636183740"],"related_works":["https://openalex.org/W2015060724","https://openalex.org/W2002102264","https://openalex.org/W3105202832","https://openalex.org/W2058578573","https://openalex.org/W2360271985","https://openalex.org/W4237964977","https://openalex.org/W3207854495","https://openalex.org/W2915353907","https://openalex.org/W2594910400","https://openalex.org/W2152429721"],"abstract_inverted_index":null,"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":2},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":3}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}
