{"id":"https://openalex.org/W2031363992","doi":"https://doi.org/10.1007/s10898-006-9122-0","title":"A geometric framework for nonconvex optimization duality using augmented lagrangian functions","display_name":"A geometric framework for nonconvex optimization duality using augmented lagrangian functions","publication_year":2006,"publication_date":"2006-12-05","ids":{"openalex":"https://openalex.org/W2031363992","doi":"https://doi.org/10.1007/s10898-006-9122-0","mag":"2031363992"},"language":"en","primary_location":{"id":"doi:10.1007/s10898-006-9122-0","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10898-006-9122-0","pdf_url":null,"source":{"id":"https://openalex.org/S115925768","display_name":"Journal of Global Optimization","issn_l":"0925-5001","issn":["0925-5001","1573-2916"],"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 Global Optimization","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/A5052663817","display_name":"Angelia Nedich","orcid":"https://orcid.org/0000-0001-9365-6321"},"institutions":[{"id":"https://openalex.org/I157725225","display_name":"University of Illinois Urbana-Champaign","ror":"https://ror.org/047426m28","country_code":"US","type":"education","lineage":["https://openalex.org/I157725225"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Angelia Nedich","raw_affiliation_strings":["Department of Industrial and Enterprise Systems Engineering, University of Illinois, Urbana, IL, USA","Department of Industrial and Enterprise Systems Engineering, University of Illinois, Urbana, USA#TAB#"],"affiliations":[{"raw_affiliation_string":"Department of Industrial and Enterprise Systems Engineering, University of Illinois, Urbana, IL, USA","institution_ids":["https://openalex.org/I157725225"]},{"raw_affiliation_string":"Department of Industrial and Enterprise Systems Engineering, University of Illinois, Urbana, USA#TAB#","institution_ids":["https://openalex.org/I157725225"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5067307504","display_name":"Asuman Ozdaglar","orcid":"https://orcid.org/0000-0002-1827-1285"},"institutions":[{"id":"https://openalex.org/I63966007","display_name":"Massachusetts Institute of Technology","ror":"https://ror.org/042nb2s44","country_code":"US","type":"education","lineage":["https://openalex.org/I63966007"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Asuman Ozdaglar","raw_affiliation_strings":["Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology, Cambridge, MA, USA","Department of Electrical Engineering & Computer Science, Massachusetts Institute of Technology, Cambridge, USA"],"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology, Cambridge, MA, USA","institution_ids":["https://openalex.org/I63966007"]},{"raw_affiliation_string":"Department of Electrical Engineering & Computer Science, Massachusetts Institute of Technology, Cambridge, USA","institution_ids":["https://openalex.org/I63966007"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5052663817"],"corresponding_institution_ids":["https://openalex.org/I157725225"],"apc_list":{"value":2190,"currency":"EUR","value_usd":2780},"apc_paid":null,"fwci":2.3663,"has_fulltext":false,"cited_by_count":34,"citation_normalized_percentile":{"value":0.88158777,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"40","issue":"4","first_page":"545","last_page":"573"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10545","display_name":"Optimization and Variational Analysis","score":0.9997000098228455,"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":0.9997000098228455,"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":0.9986000061035156,"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/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9799000024795532,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/augmented-lagrangian-method","display_name":"Augmented Lagrangian method","score":0.8317679762840271},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8277443647384644},{"id":"https://openalex.org/keywords/duality","display_name":"Duality (order theory)","score":0.773059606552124},{"id":"https://openalex.org/keywords/penalty-method","display_name":"Penalty method","score":0.6676440834999084},{"id":"https://openalex.org/keywords/strong-duality","display_name":"Strong duality","score":0.6448438763618469},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.6263259649276733},{"id":"https://openalex.org/keywords/duality-gap","display_name":"Duality gap","score":0.5961018800735474},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.5445225238800049},{"id":"https://openalex.org/keywords/lagrangian","display_name":"Lagrangian","score":0.5246003866195679},{"id":"https://openalex.org/keywords/optimization-problem","display_name":"Optimization problem","score":0.49297571182250977},{"id":"https://openalex.org/keywords/dual","display_name":"Dual (grammatical number)","score":0.4876364767551422},{"id":"https://openalex.org/keywords/lagrangian-relaxation","display_name":"Lagrangian relaxation","score":0.4638322591781616},{"id":"https://openalex.org/keywords/geometric-programming","display_name":"Geometric programming","score":0.4465218186378479},{"id":"https://openalex.org/keywords/perturbation-function","display_name":"Perturbation function","score":0.44403570890426636},{"id":"https://openalex.org/keywords/constrained-optimization-problem","display_name":"Constrained optimization problem","score":0.4365849792957306},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.38216036558151245},{"id":"https://openalex.org/keywords/convex-analysis","display_name":"Convex analysis","score":0.25095635652542114},{"id":"https://openalex.org/keywords/convex-optimization","display_name":"Convex optimization","score":0.18782535195350647},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.12416839599609375},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.10427796840667725},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.05617338418960571}],"concepts":[{"id":"https://openalex.org/C150452318","wikidata":"https://www.wikidata.org/wiki/Q4820432","display_name":"Augmented Lagrangian method","level":2,"score":0.8317679762840271},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8277443647384644},{"id":"https://openalex.org/C2778023678","wikidata":"https://www.wikidata.org/wiki/Q554403","display_name":"Duality (order theory)","level":2,"score":0.773059606552124},{"id":"https://openalex.org/C6180225","wikidata":"https://www.wikidata.org/wiki/Q3411771","display_name":"Penalty method","level":2,"score":0.6676440834999084},{"id":"https://openalex.org/C163863214","wikidata":"https://www.wikidata.org/wiki/Q7624553","display_name":"Strong duality","level":3,"score":0.6448438763618469},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.6263259649276733},{"id":"https://openalex.org/C5274546","wikidata":"https://www.wikidata.org/wiki/Q5310264","display_name":"Duality gap","level":3,"score":0.5961018800735474},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5445225238800049},{"id":"https://openalex.org/C53469067","wikidata":"https://www.wikidata.org/wiki/Q505735","display_name":"Lagrangian","level":2,"score":0.5246003866195679},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.49297571182250977},{"id":"https://openalex.org/C2780980858","wikidata":"https://www.wikidata.org/wiki/Q110022","display_name":"Dual (grammatical number)","level":2,"score":0.4876364767551422},{"id":"https://openalex.org/C91765299","wikidata":"https://www.wikidata.org/wiki/Q3424292","display_name":"Lagrangian relaxation","level":2,"score":0.4638322591781616},{"id":"https://openalex.org/C20729856","wikidata":"https://www.wikidata.org/wiki/Q2078279","display_name":"Geometric programming","level":2,"score":0.4465218186378479},{"id":"https://openalex.org/C102144036","wikidata":"https://www.wikidata.org/wiki/Q7170952","display_name":"Perturbation function","level":5,"score":0.44403570890426636},{"id":"https://openalex.org/C2989514635","wikidata":"https://www.wikidata.org/wiki/Q5164377","display_name":"Constrained optimization problem","level":3,"score":0.4365849792957306},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.38216036558151245},{"id":"https://openalex.org/C12108790","wikidata":"https://www.wikidata.org/wiki/Q2234833","display_name":"Convex analysis","level":4,"score":0.25095635652542114},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.18782535195350647},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.12416839599609375},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.10427796840667725},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.05617338418960571},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"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/C142362112","wikidata":"https://www.wikidata.org/wiki/Q735","display_name":"Art","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s10898-006-9122-0","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10898-006-9122-0","pdf_url":null,"source":{"id":"https://openalex.org/S115925768","display_name":"Journal of Global Optimization","issn_l":"0925-5001","issn":["0925-5001","1573-2916"],"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 Global Optimization","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":21,"referenced_works":["https://openalex.org/W182881619","https://openalex.org/W1499439642","https://openalex.org/W1514382660","https://openalex.org/W1553702074","https://openalex.org/W1568288633","https://openalex.org/W1583497301","https://openalex.org/W1601741115","https://openalex.org/W1966394100","https://openalex.org/W2011243226","https://openalex.org/W2123014493","https://openalex.org/W2133374626","https://openalex.org/W2266946488","https://openalex.org/W2502393534","https://openalex.org/W2798766386","https://openalex.org/W3158532942","https://openalex.org/W4242766606","https://openalex.org/W4249513058","https://openalex.org/W4249667877","https://openalex.org/W4302155765","https://openalex.org/W6635018136","https://openalex.org/W6750230808"],"related_works":["https://openalex.org/W2725387418","https://openalex.org/W2089042254","https://openalex.org/W2025430946","https://openalex.org/W1687657632","https://openalex.org/W2155425983","https://openalex.org/W640885572","https://openalex.org/W2080941243","https://openalex.org/W2325192077","https://openalex.org/W2605451175","https://openalex.org/W1979971434"],"abstract_inverted_index":null,"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":4},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":2},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}