{"id":"https://openalex.org/W2131570268","doi":"https://doi.org/10.1080/10556780701374633","title":"Limiting behavior of the Alizadeh\u2013Haeberly\u2013Overton weighted paths in semidefinite programming","display_name":"Limiting behavior of the Alizadeh\u2013Haeberly\u2013Overton weighted paths in semidefinite programming","publication_year":2007,"publication_date":"2007-08-22","ids":{"openalex":"https://openalex.org/W2131570268","doi":"https://doi.org/10.1080/10556780701374633","mag":"2131570268"},"language":"en","primary_location":{"id":"doi:10.1080/10556780701374633","is_oa":false,"landing_page_url":"https://doi.org/10.1080/10556780701374633","pdf_url":null,"source":{"id":"https://openalex.org/S103047102","display_name":"Optimization methods & software","issn_l":"1026-7670","issn":["1026-7670","1029-4937","1055-6788"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Optimization Methods and Software","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/A5000609407","display_name":"Zhaosong Lu","orcid":"https://orcid.org/0000-0003-3277-7853"},"institutions":[{"id":"https://openalex.org/I141945490","display_name":"University of British Columbia","ror":"https://ror.org/03rmrcq20","country_code":"CA","type":"education","lineage":["https://openalex.org/I141945490"]},{"id":"https://openalex.org/I18014758","display_name":"Simon Fraser University","ror":"https://ror.org/0213rcc28","country_code":"CA","type":"education","lineage":["https://openalex.org/I18014758"]}],"countries":["CA"],"is_corresponding":true,"raw_author_name":"Zhaosong Lu","raw_affiliation_strings":["Department of Mathematics, Simon Fraser University, British Columbia, V&A 156, Canada","Department of Mathematics Simon Fraser University British Columbia, Canada"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Simon Fraser University, British Columbia, V&A 156, Canada","institution_ids":["https://openalex.org/I18014758"]},{"raw_affiliation_string":"Department of Mathematics Simon Fraser University British Columbia, Canada","institution_ids":["https://openalex.org/I141945490","https://openalex.org/I18014758"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5108765688","display_name":"Renato D. C. Monteiro","orcid":null},"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":false,"raw_author_name":"Renato D. C. Monteiro","raw_affiliation_strings":["School of ISyE, Georgia Tech, Atlanta, Georgia, 30332, USA","School of ISyE, Georgia Tech, Atlanta, Georgia, USA#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of ISyE, Georgia Tech, Atlanta, Georgia, 30332, USA","institution_ids":["https://openalex.org/I130701444"]},{"raw_affiliation_string":"School of ISyE, Georgia Tech, Atlanta, Georgia, USA#TAB#","institution_ids":["https://openalex.org/I130701444"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5000609407"],"corresponding_institution_ids":["https://openalex.org/I141945490","https://openalex.org/I18014758"],"apc_list":null,"apc_paid":null,"fwci":3.467,"has_fulltext":false,"cited_by_count":17,"citation_normalized_percentile":{"value":0.92539233,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"22","issue":"5","first_page":"849","last_page":"870"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9998999834060669,"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":0.9998999834060669,"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/T10545","display_name":"Optimization and Variational Analysis","score":0.9857000112533569,"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/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.961899995803833,"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/semidefinite-programming","display_name":"Semidefinite programming","score":0.8304674029350281},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8190588355064392},{"id":"https://openalex.org/keywords/interior-point-method","display_name":"Interior point method","score":0.7742680311203003},{"id":"https://openalex.org/keywords/semidefinite-embedding","display_name":"Semidefinite embedding","score":0.6234966516494751},{"id":"https://openalex.org/keywords/path","display_name":"Path (computing)","score":0.4963863492012024},{"id":"https://openalex.org/keywords/quadratically-constrained-quadratic-program","display_name":"Quadratically constrained quadratic program","score":0.47513821721076965},{"id":"https://openalex.org/keywords/positive-definite-matrix","display_name":"Positive-definite matrix","score":0.47433608770370483},{"id":"https://openalex.org/keywords/linear-programming","display_name":"Linear programming","score":0.4662439227104187},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.45000672340393066},{"id":"https://openalex.org/keywords/limit-point","display_name":"Limit point","score":0.4200096130371094},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.41638708114624023},{"id":"https://openalex.org/keywords/limiting","display_name":"Limiting","score":0.41516488790512085},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.404039591550827},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.37403857707977295},{"id":"https://openalex.org/keywords/quadratic-programming","display_name":"Quadratic programming","score":0.29682761430740356},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.1568484604358673},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.11141049861907959},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.07694265246391296}],"concepts":[{"id":"https://openalex.org/C101901036","wikidata":"https://www.wikidata.org/wiki/Q2269096","display_name":"Semidefinite programming","level":2,"score":0.8304674029350281},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8190588355064392},{"id":"https://openalex.org/C155253501","wikidata":"https://www.wikidata.org/wiki/Q461992","display_name":"Interior point method","level":2,"score":0.7742680311203003},{"id":"https://openalex.org/C206818286","wikidata":"https://www.wikidata.org/wiki/Q7449403","display_name":"Semidefinite embedding","level":4,"score":0.6234966516494751},{"id":"https://openalex.org/C2777735758","wikidata":"https://www.wikidata.org/wiki/Q817765","display_name":"Path (computing)","level":2,"score":0.4963863492012024},{"id":"https://openalex.org/C65148998","wikidata":"https://www.wikidata.org/wiki/Q7268373","display_name":"Quadratically constrained quadratic program","level":3,"score":0.47513821721076965},{"id":"https://openalex.org/C49712288","wikidata":"https://www.wikidata.org/wiki/Q77601250","display_name":"Positive-definite matrix","level":3,"score":0.47433608770370483},{"id":"https://openalex.org/C41045048","wikidata":"https://www.wikidata.org/wiki/Q202843","display_name":"Linear programming","level":2,"score":0.4662439227104187},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.45000672340393066},{"id":"https://openalex.org/C63548660","wikidata":"https://www.wikidata.org/wiki/Q858223","display_name":"Limit point","level":2,"score":0.4200096130371094},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.41638708114624023},{"id":"https://openalex.org/C188198153","wikidata":"https://www.wikidata.org/wiki/Q1613840","display_name":"Limiting","level":2,"score":0.41516488790512085},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.404039591550827},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.37403857707977295},{"id":"https://openalex.org/C81845259","wikidata":"https://www.wikidata.org/wiki/Q290117","display_name":"Quadratic programming","level":2,"score":0.29682761430740356},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.1568484604358673},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.11141049861907959},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.07694265246391296},{"id":"https://openalex.org/C78519656","wikidata":"https://www.wikidata.org/wiki/Q101333","display_name":"Mechanical engineering","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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1080/10556780701374633","is_oa":false,"landing_page_url":"https://doi.org/10.1080/10556780701374633","pdf_url":null,"source":{"id":"https://openalex.org/S103047102","display_name":"Optimization methods & software","issn_l":"1026-7670","issn":["1026-7670","1029-4937","1055-6788"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Optimization Methods and Software","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":48,"referenced_works":["https://openalex.org/W1487405513","https://openalex.org/W1495980450","https://openalex.org/W1518039036","https://openalex.org/W1570961610","https://openalex.org/W1573409602","https://openalex.org/W1588330761","https://openalex.org/W1963924267","https://openalex.org/W1966000604","https://openalex.org/W1967960319","https://openalex.org/W1969707050","https://openalex.org/W1977327182","https://openalex.org/W1993891506","https://openalex.org/W1994350792","https://openalex.org/W2003324738","https://openalex.org/W2012110988","https://openalex.org/W2017954027","https://openalex.org/W2023381926","https://openalex.org/W2025444228","https://openalex.org/W2025486357","https://openalex.org/W2025617394","https://openalex.org/W2026418020","https://openalex.org/W2033597467","https://openalex.org/W2046872182","https://openalex.org/W2049928456","https://openalex.org/W2059352176","https://openalex.org/W2064462686","https://openalex.org/W2068649881","https://openalex.org/W2069798394","https://openalex.org/W2072165663","https://openalex.org/W2075379600","https://openalex.org/W2086250665","https://openalex.org/W2090279609","https://openalex.org/W2094584490","https://openalex.org/W2096428697","https://openalex.org/W2117973746","https://openalex.org/W2124476861","https://openalex.org/W2146371908","https://openalex.org/W2148775520","https://openalex.org/W2154089483","https://openalex.org/W2165785900","https://openalex.org/W2169647923","https://openalex.org/W2188855303","https://openalex.org/W2334285086","https://openalex.org/W2572487493","https://openalex.org/W2971268466","https://openalex.org/W4206734951","https://openalex.org/W4210281310","https://openalex.org/W4256500882"],"related_works":["https://openalex.org/W2348903644","https://openalex.org/W2975050997","https://openalex.org/W2737505353","https://openalex.org/W2912522929","https://openalex.org/W1653317167","https://openalex.org/W1989828432","https://openalex.org/W2364528045","https://openalex.org/W2352839224","https://openalex.org/W2385886188","https://openalex.org/W2461836650"],"abstract_inverted_index":{"This":[0],"paper":[1],"studies":[2],"the":[3,19,39,42,59,104,107,111,128,139,143,155],"limiting":[4],"behavior":[5],"of":[6,18,73,94,106,110,138,145,158],"weighted":[7,88],"infeasible":[8],"central":[9,89,140],"paths":[10,75],"for":[11,154],"semidefinite":[12,78],"programming":[13],"obtained":[14],"from":[15],"centrality":[16],"equations":[17],"form":[20],"X":[21],"S+SX=2":[22],"\u03bd":[23,95],"W,":[24],"where":[25],"W":[26],"is":[27,35,118],"a":[28,36,45,53,87,92,131,135],"fixed":[29],"positive":[30],"definite":[31],"matrix":[32],"and":[33,55,64,68,113,142],"\u03bd>0":[34],"parameter,":[37],"under":[38],"assumption":[40],"that":[41,86],"problem":[43],"has":[44],"strictly":[46],"complementary":[47],"primal\u2013dual":[48,146,160],"optimal":[49,147],"solution.":[50],"We":[51,121],"present":[52],"different":[54],"simpler":[56],"proof":[57],"than":[58],"one":[60],"given":[61],"by":[62],"Prei\u00df":[63],"Stoer":[65],"[Prei\u00df,":[66],"M.":[67],"Stoer,":[69],"J.,":[70],"2004,":[71],"Analysis":[72],"infeasible-interior-point":[74],"arising":[76],"with":[77],"linear":[79],"complementarity":[80],"problems.":[81],"Mathematical":[82],"Programming":[83],"99,":[84],"499\u2013520.]":[85],"path":[90,112,141],"as":[91],"function":[93],"can":[96],"be":[97],"extended":[98],"analytically":[99],"beyond":[100],"0.":[101],"In":[102],"addition,":[103],"characterization":[105],"limit":[108],"points":[109],"its":[114],"normalized":[115],"first-order":[116],"derivatives":[117],"also":[119,122],"provided.":[120],"derive":[123],"an":[124],"error":[125],"bound":[126],"on":[127],"distance":[129],"between":[130],"point":[132,162],"lying":[133],"in":[134],"certain":[136],"neighborhood":[137],"set":[144],"solutions.":[148],"Finally,":[149],"we":[150],"make":[151],"some":[152,159],"observation":[153],"superlinear":[156],"convergence":[157],"interior":[161],"SDP":[163],"algorithms":[164],"using":[165],"AHO":[166],"neighborhood.":[167]},"counts_by_year":[{"year":2018,"cited_by_count":3},{"year":2016,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2012,"cited_by_count":2}],"updated_date":"2026-07-29T09:40:50.615796","created_date":"2025-10-10T00:00:00"}
