{"id":"https://openalex.org/W2070812009","doi":"https://doi.org/10.1007/s10107-006-0020-5","title":"Multiplier convergence in trust-region methods with application to convergence of decomposition methods for MPECs","display_name":"Multiplier convergence in trust-region methods with application to convergence of decomposition methods for MPECs","publication_year":2006,"publication_date":"2006-09-01","ids":{"openalex":"https://openalex.org/W2070812009","doi":"https://doi.org/10.1007/s10107-006-0020-5","mag":"2070812009"},"language":"en","primary_location":{"id":"doi:10.1007/s10107-006-0020-5","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10107-006-0020-5","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/A5058243487","display_name":"Giovanni Giallombardo","orcid":"https://orcid.org/0000-0002-3714-197X"},"institutions":[{"id":"https://openalex.org/I45204951","display_name":"University of Calabria","ror":"https://ror.org/02rc97e94","country_code":"IT","type":"education","lineage":["https://openalex.org/I45204951"]}],"countries":["IT"],"is_corresponding":true,"raw_author_name":"Giovanni Giallombardo","raw_affiliation_strings":["Dipartimento di Elettronica, Informatica e Sistemistica, Universit\u00e0 della Calabria, 87036, Rende (CS), Italy","Universit\u00e0 della Calabria, Dipartimento di Elettronica Informatica e Sistemistica, 87036, Rende (CS), Italy#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Dipartimento di Elettronica, Informatica e Sistemistica, Universit\u00e0 della Calabria, 87036, Rende (CS), Italy","institution_ids":["https://openalex.org/I45204951"]},{"raw_affiliation_string":"Universit\u00e0 della Calabria, Dipartimento di Elettronica Informatica e Sistemistica, 87036, Rende (CS), Italy#TAB#","institution_ids":["https://openalex.org/I45204951"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5102776002","display_name":"Daniel Ralph","orcid":"https://orcid.org/0000-0002-1079-4081"},"institutions":[{"id":"https://openalex.org/I241749","display_name":"University of Cambridge","ror":"https://ror.org/013meh722","country_code":"GB","type":"education","lineage":["https://openalex.org/I241749"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Daniel Ralph","raw_affiliation_strings":["Judge Business School, University of Cambridge, Cambridge, CB2 1AG, UK","University of Cambridge, Judge Business School, CB2 1AG, Cambridge, UK#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Judge Business School, University of Cambridge, Cambridge, CB2 1AG, UK","institution_ids":["https://openalex.org/I241749"]},{"raw_affiliation_string":"University of Cambridge, Judge Business School, CB2 1AG, Cambridge, UK#TAB#","institution_ids":["https://openalex.org/I241749"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5058243487"],"corresponding_institution_ids":["https://openalex.org/I45204951"],"apc_list":{"value":2890,"currency":"USD","value_usd":2890},"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":17,"citation_normalized_percentile":{"value":0.14380531,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"112","issue":"2","first_page":"335","last_page":"369"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9990000128746033,"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":0.9990000128746033,"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/T10792","display_name":"Matrix Theory and Algorithms","score":0.9965000152587891,"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":0.9934999942779541,"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/trust-region","display_name":"Trust region","score":0.9478316307067871},{"id":"https://openalex.org/keywords/solver","display_name":"Solver","score":0.7029072046279907},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6726637482643127},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.6140891313552856},{"id":"https://openalex.org/keywords/robustness","display_name":"Robustness (evolution)","score":0.5952145457267761},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.5913688540458679},{"id":"https://openalex.org/keywords/multiplier","display_name":"Multiplier (economics)","score":0.5900746583938599},{"id":"https://openalex.org/keywords/nonlinear-programming","display_name":"Nonlinear programming","score":0.5899623036384583},{"id":"https://openalex.org/keywords/piecewise","display_name":"Piecewise","score":0.49732449650764465},{"id":"https://openalex.org/keywords/decomposition-method","display_name":"Decomposition method (queueing theory)","score":0.4635692238807678},{"id":"https://openalex.org/keywords/symbolic-convergence-theory","display_name":"Symbolic convergence theory","score":0.4553232491016388},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.4524752199649811},{"id":"https://openalex.org/keywords/lagrange-multiplier","display_name":"Lagrange multiplier","score":0.44699960947036743},{"id":"https://openalex.org/keywords/compact-convergence","display_name":"Compact convergence","score":0.4414002299308777},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.23370260000228882},{"id":"https://openalex.org/keywords/rate-of-convergence","display_name":"Rate of convergence","score":0.20813488960266113},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.061941325664520264},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.05388614535331726}],"concepts":[{"id":"https://openalex.org/C89109886","wikidata":"https://www.wikidata.org/wiki/Q1535924","display_name":"Trust region","level":3,"score":0.9478316307067871},{"id":"https://openalex.org/C2778770139","wikidata":"https://www.wikidata.org/wiki/Q1966904","display_name":"Solver","level":2,"score":0.7029072046279907},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6726637482643127},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.6140891313552856},{"id":"https://openalex.org/C63479239","wikidata":"https://www.wikidata.org/wiki/Q7353546","display_name":"Robustness (evolution)","level":3,"score":0.5952145457267761},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5913688540458679},{"id":"https://openalex.org/C124584101","wikidata":"https://www.wikidata.org/wiki/Q1053266","display_name":"Multiplier (economics)","level":2,"score":0.5900746583938599},{"id":"https://openalex.org/C115527620","wikidata":"https://www.wikidata.org/wiki/Q769909","display_name":"Nonlinear programming","level":3,"score":0.5899623036384583},{"id":"https://openalex.org/C164660894","wikidata":"https://www.wikidata.org/wiki/Q2037833","display_name":"Piecewise","level":2,"score":0.49732449650764465},{"id":"https://openalex.org/C2778258933","wikidata":"https://www.wikidata.org/wiki/Q16918986","display_name":"Decomposition method (queueing theory)","level":2,"score":0.4635692238807678},{"id":"https://openalex.org/C64980692","wikidata":"https://www.wikidata.org/wiki/Q16191959","display_name":"Symbolic convergence theory","level":3,"score":0.4553232491016388},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.4524752199649811},{"id":"https://openalex.org/C73684929","wikidata":"https://www.wikidata.org/wiki/Q598870","display_name":"Lagrange multiplier","level":2,"score":0.44699960947036743},{"id":"https://openalex.org/C5871375","wikidata":"https://www.wikidata.org/wiki/Q1780715","display_name":"Compact convergence","level":4,"score":0.4414002299308777},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.23370260000228882},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.20813488960266113},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.061941325664520264},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.05388614535331726},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C38652104","wikidata":"https://www.wikidata.org/wiki/Q3510521","display_name":"Computer security","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C127162648","wikidata":"https://www.wikidata.org/wiki/Q16858953","display_name":"Channel (broadcasting)","level":2,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C139719470","wikidata":"https://www.wikidata.org/wiki/Q39680","display_name":"Macroeconomics","level":1,"score":0.0},{"id":"https://openalex.org/C178635117","wikidata":"https://www.wikidata.org/wiki/Q747499","display_name":"RADIUS","level":2,"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/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C26517878","wikidata":"https://www.wikidata.org/wiki/Q228039","display_name":"Key (lock)","level":2,"score":0.0},{"id":"https://openalex.org/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/s10107-006-0020-5","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10107-006-0020-5","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:10.1.1.329.1435","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.329.1435","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.optimization-online.org/DB_FILE/2006/08/1449.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/10","score":0.41999998688697815,"display_name":"Reduced inequalities"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":55,"referenced_works":["https://openalex.org/W21446130","https://openalex.org/W65560571","https://openalex.org/W145191360","https://openalex.org/W147998453","https://openalex.org/W217831350","https://openalex.org/W635755880","https://openalex.org/W641167758","https://openalex.org/W1517656880","https://openalex.org/W1543439990","https://openalex.org/W1562374763","https://openalex.org/W1572204513","https://openalex.org/W1601741115","https://openalex.org/W1604627832","https://openalex.org/W1674199609","https://openalex.org/W1832190644","https://openalex.org/W1966095601","https://openalex.org/W1971720918","https://openalex.org/W1976886395","https://openalex.org/W1980782931","https://openalex.org/W2005604902","https://openalex.org/W2006729027","https://openalex.org/W2007444179","https://openalex.org/W2011672735","https://openalex.org/W2029564096","https://openalex.org/W2034039293","https://openalex.org/W2037678919","https://openalex.org/W2042838878","https://openalex.org/W2046272803","https://openalex.org/W2058708460","https://openalex.org/W2065066829","https://openalex.org/W2067824962","https://openalex.org/W2074352998","https://openalex.org/W2077658674","https://openalex.org/W2087472326","https://openalex.org/W2095246905","https://openalex.org/W2098132613","https://openalex.org/W2120461039","https://openalex.org/W2122587727","https://openalex.org/W2133314983","https://openalex.org/W2144027161","https://openalex.org/W2155640943","https://openalex.org/W2163319674","https://openalex.org/W2166758048","https://openalex.org/W2171126500","https://openalex.org/W2798766386","https://openalex.org/W2804014942","https://openalex.org/W3012317737","https://openalex.org/W3192527823","https://openalex.org/W3217008510","https://openalex.org/W4212997115","https://openalex.org/W4231147659","https://openalex.org/W4235178178","https://openalex.org/W4246495354","https://openalex.org/W4249667877","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W2060328336","https://openalex.org/W1980202627","https://openalex.org/W3209065746","https://openalex.org/W2543658186","https://openalex.org/W3176762001","https://openalex.org/W3157327433","https://openalex.org/W2012871340","https://openalex.org/W2389157665","https://openalex.org/W1974580502","https://openalex.org/W2070812009"],"abstract_inverted_index":null,"counts_by_year":[{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":1},{"year":2020,"cited_by_count":2},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":2},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":3}],"updated_date":"2026-07-23T08:03:31.855105","created_date":"2025-10-10T00:00:00"}
