{"id":"https://openalex.org/W1970503897","doi":"https://doi.org/10.1109/tsp.2013.2264814","title":"A Lagrangian Dual Approach to the Single-Source Localization Problem","display_name":"A Lagrangian Dual Approach to the Single-Source Localization Problem","publication_year":2013,"publication_date":"2013-05-23","ids":{"openalex":"https://openalex.org/W1970503897","doi":"https://doi.org/10.1109/tsp.2013.2264814","mag":"1970503897"},"language":"en","primary_location":{"id":"doi:10.1109/tsp.2013.2264814","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tsp.2013.2264814","pdf_url":null,"source":{"id":"https://openalex.org/S168680287","display_name":"IEEE Transactions on Signal Processing","issn_l":"1053-587X","issn":["1053-587X","1941-0476"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Signal Processing","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/A5112621269","display_name":"Houduo Qi","orcid":"https://orcid.org/0000-0003-3481-4814"},"institutions":[{"id":"https://openalex.org/I43439940","display_name":"University of Southampton","ror":"https://ror.org/01ryk1543","country_code":"GB","type":"education","lineage":["https://openalex.org/I43439940"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Hou-Duo Qi","raw_affiliation_strings":["School of Mathematics, University of Southampton, Southampton, UK","Sch. of Math., Univ. of Southampton, Southampton, UK"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics, University of Southampton, Southampton, UK","institution_ids":["https://openalex.org/I43439940"]},{"raw_affiliation_string":"Sch. of Math., Univ. of Southampton, Southampton, UK","institution_ids":["https://openalex.org/I43439940"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5071551240","display_name":"Naihua Xiu","orcid":"https://orcid.org/0000-0002-3129-2005"},"institutions":[{"id":"https://openalex.org/I21193070","display_name":"Beijing Jiaotong University","ror":"https://ror.org/01yj56c84","country_code":"CN","type":"education","lineage":["https://openalex.org/I21193070"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Naihua Xiu","raw_affiliation_strings":["Department of Applied Mathematics, Beijing Jiaotong University, Beijing, China","Dept. of Appl. Math., Beijing Jiaotong Univ., Beijing, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics, Beijing Jiaotong University, Beijing, China","institution_ids":["https://openalex.org/I21193070"]},{"raw_affiliation_string":"Dept. of Appl. Math., Beijing Jiaotong Univ., Beijing, China","institution_ids":["https://openalex.org/I21193070"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5060269704","display_name":"Xiaoming Yuan","orcid":"https://orcid.org/0000-0002-6900-6983"},"institutions":[{"id":"https://openalex.org/I141568987","display_name":"Hong Kong Baptist University","ror":"https://ror.org/0145fw131","country_code":"HK","type":"education","lineage":["https://openalex.org/I141568987"]}],"countries":["HK"],"is_corresponding":false,"raw_author_name":"Xiaoming Yuan","raw_affiliation_strings":["Department of Mathematics, Hong Kong Baptist University, Hong Kong, China","[Dept. of Math., Hong Kong Baptist Univ., Kowloon, China]"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Hong Kong Baptist University, Hong Kong, China","institution_ids":["https://openalex.org/I141568987"]},{"raw_affiliation_string":"[Dept. of Math., Hong Kong Baptist Univ., Kowloon, China]","institution_ids":["https://openalex.org/I141568987"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.8789,"has_fulltext":false,"cited_by_count":29,"citation_normalized_percentile":{"value":0.86380486,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"61","issue":"15","first_page":"3815","last_page":"3826"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10326","display_name":"Indoor and Outdoor Localization Technologies","score":1.0,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"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/T10326","display_name":"Indoor and Outdoor Localization Technologies","score":1.0,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"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/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9987000226974487,"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/T12879","display_name":"Distributed Sensor Networks and Detection Algorithms","score":0.9936000108718872,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"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/augmented-lagrangian-method","display_name":"Augmented Lagrangian method","score":0.6547608375549316},{"id":"https://openalex.org/keywords/lagrangian-relaxation","display_name":"Lagrangian relaxation","score":0.6192257404327393},{"id":"https://openalex.org/keywords/solver","display_name":"Solver","score":0.574493408203125},{"id":"https://openalex.org/keywords/lagrangian","display_name":"Lagrangian","score":0.5408592224121094},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5363045930862427},{"id":"https://openalex.org/keywords/duality","display_name":"Duality (order theory)","score":0.5360382795333862},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5321157574653625},{"id":"https://openalex.org/keywords/dual","display_name":"Dual (grammatical number)","score":0.4999704360961914},{"id":"https://openalex.org/keywords/embedding","display_name":"Embedding","score":0.49857091903686523},{"id":"https://openalex.org/keywords/euclidean-geometry","display_name":"Euclidean geometry","score":0.4231518805027008},{"id":"https://openalex.org/keywords/strong-duality","display_name":"Strong duality","score":0.4140864908695221},{"id":"https://openalex.org/keywords/euclidean-distance","display_name":"Euclidean distance","score":0.411434143781662},{"id":"https://openalex.org/keywords/optimization-problem","display_name":"Optimization problem","score":0.3958227336406708},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.335988849401474},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3273511528968811},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.13225668668746948},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.13201305270195007},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.10290947556495667}],"concepts":[{"id":"https://openalex.org/C150452318","wikidata":"https://www.wikidata.org/wiki/Q4820432","display_name":"Augmented Lagrangian method","level":2,"score":0.6547608375549316},{"id":"https://openalex.org/C91765299","wikidata":"https://www.wikidata.org/wiki/Q3424292","display_name":"Lagrangian relaxation","level":2,"score":0.6192257404327393},{"id":"https://openalex.org/C2778770139","wikidata":"https://www.wikidata.org/wiki/Q1966904","display_name":"Solver","level":2,"score":0.574493408203125},{"id":"https://openalex.org/C53469067","wikidata":"https://www.wikidata.org/wiki/Q505735","display_name":"Lagrangian","level":2,"score":0.5408592224121094},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5363045930862427},{"id":"https://openalex.org/C2778023678","wikidata":"https://www.wikidata.org/wiki/Q554403","display_name":"Duality (order theory)","level":2,"score":0.5360382795333862},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5321157574653625},{"id":"https://openalex.org/C2780980858","wikidata":"https://www.wikidata.org/wiki/Q110022","display_name":"Dual (grammatical number)","level":2,"score":0.4999704360961914},{"id":"https://openalex.org/C41608201","wikidata":"https://www.wikidata.org/wiki/Q980509","display_name":"Embedding","level":2,"score":0.49857091903686523},{"id":"https://openalex.org/C129782007","wikidata":"https://www.wikidata.org/wiki/Q162886","display_name":"Euclidean geometry","level":2,"score":0.4231518805027008},{"id":"https://openalex.org/C163863214","wikidata":"https://www.wikidata.org/wiki/Q7624553","display_name":"Strong duality","level":3,"score":0.4140864908695221},{"id":"https://openalex.org/C120174047","wikidata":"https://www.wikidata.org/wiki/Q847073","display_name":"Euclidean distance","level":2,"score":0.411434143781662},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.3958227336406708},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.335988849401474},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3273511528968811},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.13225668668746948},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.13201305270195007},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.10290947556495667},{"id":"https://openalex.org/C142362112","wikidata":"https://www.wikidata.org/wiki/Q735","display_name":"Art","level":0,"score":0.0},{"id":"https://openalex.org/C124952713","wikidata":"https://www.wikidata.org/wiki/Q8242","display_name":"Literature","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1109/tsp.2013.2264814","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tsp.2013.2264814","pdf_url":null,"source":{"id":"https://openalex.org/S168680287","display_name":"IEEE Transactions on Signal Processing","issn_l":"1053-587X","issn":["1053-587X","1941-0476"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Signal Processing","raw_type":"journal-article"},{"id":"pmh:oai:eprints.soton.ac.uk:358009","is_oa":false,"landing_page_url":"https://eprints.soton.ac.uk/358009/1/TSP2264814final.pdf","pdf_url":null,"source":{"id":"https://openalex.org/S4306401019","display_name":"ePrints Soton (University of Southampton)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I43439940","host_organization_name":"University of Southampton","host_organization_lineage":["https://openalex.org/I43439940"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":"","raw_type":"Article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.306.3722","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.306.3722","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.personal.soton.ac.uk/hdqi/REPORTS/SSLP.pdf","raw_type":"text"},{"id":"pmh:oai:hub.hku.hk:10722/250869","is_oa":false,"landing_page_url":"http://hdl.handle.net/10722/250869","pdf_url":null,"source":{"id":"https://openalex.org/S4377196271","display_name":"The HKU Scholars Hub (University of Hong Kong)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I889458895","host_organization_name":"University of Hong Kong","host_organization_lineage":["https://openalex.org/I889458895"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1261773691","display_name":null,"funder_award_id":"EP/K007645/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G4634565378","display_name":"\u591a\u7ef4\u6807\u5ea6\u95ee\u9898\u7684\u77e9\u9635\u4f18\u5316\u6a21\u578b\u4e0e\u7b97\u6cd5\u7814\u7a76","funder_award_id":"71271021","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320334627","display_name":"Engineering and Physical Sciences Research Council","ror":"https://ror.org/0439y7842"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":31,"referenced_works":["https://openalex.org/W91728630","https://openalex.org/W765936379","https://openalex.org/W1551360398","https://openalex.org/W1964922595","https://openalex.org/W1984910745","https://openalex.org/W1989148040","https://openalex.org/W1990908167","https://openalex.org/W2000389722","https://openalex.org/W2003250847","https://openalex.org/W2007304358","https://openalex.org/W2009271970","https://openalex.org/W2037261607","https://openalex.org/W2037402401","https://openalex.org/W2039715928","https://openalex.org/W2040055413","https://openalex.org/W2044541911","https://openalex.org/W2049444669","https://openalex.org/W2061681393","https://openalex.org/W2067752346","https://openalex.org/W2091850740","https://openalex.org/W2107376953","https://openalex.org/W2125947724","https://openalex.org/W2133353795","https://openalex.org/W2144467430","https://openalex.org/W2151568819","https://openalex.org/W2163392119","https://openalex.org/W2163817142","https://openalex.org/W2327230547","https://openalex.org/W2953018250","https://openalex.org/W3022413497","https://openalex.org/W3046579346"],"related_works":["https://openalex.org/W2360271985","https://openalex.org/W2131718214","https://openalex.org/W3149469165","https://openalex.org/W2002987466","https://openalex.org/W2070276483","https://openalex.org/W4313484281","https://openalex.org/W1972437117","https://openalex.org/W4383905034","https://openalex.org/W1973889396","https://openalex.org/W2467306310"],"abstract_inverted_index":{"The":[0],"single-source":[1],"localization":[2,135,147,167],"problem":[3,37,51,168],"(SSLP),":[4],"which":[5],"is":[6,45],"nonconvex":[7],"by":[8,89,119],"its":[9],"nature,":[10],"appears":[11],"in":[12],"several":[13],"important":[14],"multidisciplinary":[15],"fields":[16],"such":[17],"as":[18,32,151],"signal":[19],"processing":[20],"and":[21,38,71,80,94,154],"the":[22,48,58,68,73,76,81,116,120,124,133,141,152,158,164,170],"global":[23],"positioning":[24],"system.":[25],"In":[26],"this":[27],"paper,":[28],"we":[29],"cast":[30],"SSLP":[31],"a":[33,40,64,129],"Euclidean":[34],"distance":[35],"embedding":[36],"study":[39],"Lagrangian":[41,49,77,125,142],"dual":[42,50,78,126,143],"approach.":[43,122],"It":[44],"proved":[46],"that":[47,140],"must":[52],"have":[53],"an":[54],"optimal":[55],"solution":[56],"under":[57],"generalized":[59],"Slater":[60],"condition.":[61],"We":[62,110],"provide":[63],"sufficient":[65],"condition":[66],"for":[67,163],"zero-duality":[69],"gap":[70],"establish":[72],"equivalence":[74],"between":[75],"approach":[79,87,127,144],"existing":[82],"Generalized":[83],"Trust-Region":[84],"Subproblem":[85],"(GTRS)":[86],"studied":[88],"Beck":[90],"et":[91],"al.":[92],"[\u201cExact":[93],"Approximate":[95],"Solutions":[96],"of":[97,115,148],"Source":[98],"Localization":[99],"Problems,\u201d":[100],"IEEE":[101],"Trans.":[102],"Signal":[103],"Process.,":[104],"vol.":[105],"56,":[106],"pp.":[107],"1770-1778,":[108],"2008].":[109],"also":[111],"reveal":[112],"new":[113],"implications":[114],"assumptions":[117],"made":[118],"GTRS":[121,153],"Moreover,":[123],"has":[128],"straightforward":[130],"extension":[131],"to":[132],"multiple-source":[134],"problem.":[136],"Numerical":[137],"simulations":[138],"demonstrate":[139],"can":[145,155],"produce":[146],"similar":[149],"quality":[150],"significantly":[156],"outperform":[157],"well-known":[159],"semidefinite":[160],"programming":[161],"solver":[162],"multiple":[165],"source":[166],"on":[169],"tested":[171],"cases.":[172]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":6},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":3},{"year":2014,"cited_by_count":3},{"year":2013,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}