{"id":"https://openalex.org/W2121787677","doi":"https://doi.org/10.1109/tsp.2011.2162507","title":"Semidefinite Relaxations of Robust Binary Least Squares Under Ellipsoidal Uncertainty Sets","display_name":"Semidefinite Relaxations of Robust Binary Least Squares Under Ellipsoidal Uncertainty Sets","publication_year":2011,"publication_date":"2011-07-26","ids":{"openalex":"https://openalex.org/W2121787677","doi":"https://doi.org/10.1109/tsp.2011.2162507","mag":"2121787677"},"language":"en","primary_location":{"id":"doi:10.1109/tsp.2011.2162507","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tsp.2011.2162507","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/A5085696978","display_name":"Efthymios Tsakonas","orcid":null},"institutions":[{"id":"https://openalex.org/I86987016","display_name":"KTH Royal Institute of Technology","ror":"https://ror.org/026vcq606","country_code":"SE","type":"education","lineage":["https://openalex.org/I86987016"]}],"countries":["SE"],"is_corresponding":true,"raw_author_name":"E. E. Tsakonas","raw_affiliation_strings":["ACCESS Linnaeus Centre, Royal Institute of Technology (KTH), Stockholm, Sweden","ACCESS Linnaeus Centre, R. Inst. of Technol. (KTH), Stockholm, Sweden"],"affiliations":[{"raw_affiliation_string":"ACCESS Linnaeus Centre, Royal Institute of Technology (KTH), Stockholm, Sweden","institution_ids":["https://openalex.org/I86987016"]},{"raw_affiliation_string":"ACCESS Linnaeus Centre, R. Inst. of Technol. (KTH), Stockholm, Sweden","institution_ids":["https://openalex.org/I86987016"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5059936184","display_name":"Joakim Jald\u00e9n","orcid":"https://orcid.org/0000-0001-6630-243X"},"institutions":[{"id":"https://openalex.org/I86987016","display_name":"KTH Royal Institute of Technology","ror":"https://ror.org/026vcq606","country_code":"SE","type":"education","lineage":["https://openalex.org/I86987016"]}],"countries":["SE"],"is_corresponding":false,"raw_author_name":"J. Jalden","raw_affiliation_strings":["ACCESS Linnaeus Centre, Royal Institute of Technology (KTH), Stockholm, Sweden","ACCESS Linnaeus Centre, R. Inst. of Technol. (KTH), Stockholm, Sweden"],"affiliations":[{"raw_affiliation_string":"ACCESS Linnaeus Centre, Royal Institute of Technology (KTH), Stockholm, Sweden","institution_ids":["https://openalex.org/I86987016"]},{"raw_affiliation_string":"ACCESS Linnaeus Centre, R. Inst. of Technol. (KTH), Stockholm, Sweden","institution_ids":["https://openalex.org/I86987016"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5080037825","display_name":"Bj\u00f6rn Ottersten","orcid":"https://orcid.org/0000-0003-2298-6774"},"institutions":[{"id":"https://openalex.org/I186903577","display_name":"University of Luxembourg","ror":"https://ror.org/036x5ad56","country_code":"LU","type":"education","lineage":["https://openalex.org/I186903577"]}],"countries":["LU"],"is_corresponding":false,"raw_author_name":"B. Ottersten","raw_affiliation_strings":["Interdisciplinary Centre for Security, Reliability and Trust, University of Luxembourg, Luxembourg","Interdiscipl. Centre for Security, Reliability, & Trust, Univ. of Luxembourg, Luxembourg, Luxembourg"],"affiliations":[{"raw_affiliation_string":"Interdisciplinary Centre for Security, Reliability and Trust, University of Luxembourg, Luxembourg","institution_ids":["https://openalex.org/I186903577"]},{"raw_affiliation_string":"Interdiscipl. Centre for Security, Reliability, & Trust, Univ. of Luxembourg, Luxembourg, Luxembourg","institution_ids":["https://openalex.org/I186903577"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5085696978"],"corresponding_institution_ids":["https://openalex.org/I86987016"],"apc_list":null,"apc_paid":null,"fwci":1.5499,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":{"value":0.86523364,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"59","issue":"11","first_page":"5169","last_page":"5180"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10928","display_name":"Probabilistic and Robust Engineering Design","score":0.9991999864578247,"subfield":{"id":"https://openalex.org/subfields/1804","display_name":"Statistics, Probability and Uncertainty"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},"topics":[{"id":"https://openalex.org/T10928","display_name":"Probabilistic and Robust Engineering Design","score":0.9991999864578247,"subfield":{"id":"https://openalex.org/subfields/1804","display_name":"Statistics, Probability and Uncertainty"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9980999827384949,"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/T11413","display_name":"Risk and Portfolio Optimization","score":0.9950000047683716,"subfield":{"id":"https://openalex.org/subfields/1803","display_name":"Management Science and Operations Research"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/notation","display_name":"Notation","score":0.6554443836212158},{"id":"https://openalex.org/keywords/ellipsoid","display_name":"Ellipsoid","score":0.5943126082420349},{"id":"https://openalex.org/keywords/binary-number","display_name":"Binary number","score":0.5717647075653076},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5002148151397705},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.474186509847641},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.45996788144111633},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4060284495353699},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3948766589164734},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.34163698554039},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.12374255061149597},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.10861748456954956},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.07325589656829834}],"concepts":[{"id":"https://openalex.org/C45357846","wikidata":"https://www.wikidata.org/wiki/Q2001982","display_name":"Notation","level":2,"score":0.6554443836212158},{"id":"https://openalex.org/C57489055","wikidata":"https://www.wikidata.org/wiki/Q190046","display_name":"Ellipsoid","level":2,"score":0.5943126082420349},{"id":"https://openalex.org/C48372109","wikidata":"https://www.wikidata.org/wiki/Q3913","display_name":"Binary number","level":2,"score":0.5717647075653076},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5002148151397705},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.474186509847641},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.45996788144111633},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4060284495353699},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3948766589164734},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.34163698554039},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.12374255061149597},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.10861748456954956},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.07325589656829834},{"id":"https://openalex.org/C1276947","wikidata":"https://www.wikidata.org/wiki/Q333","display_name":"Astronomy","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/tsp.2011.2162507","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tsp.2011.2162507","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:orbilu.uni.lu:10993/7590","is_oa":false,"landing_page_url":"https://orbilu.uni.lu/handle/10993/7590","pdf_url":null,"source":{"id":"https://openalex.org/S4306401815","display_name":"Open Repository and Bibliography (University of Luxembourg)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I186903577","host_organization_name":"University of Luxembourg","host_organization_lineage":["https://openalex.org/I186903577"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"IEEE Transactions on Signal Processing, 59 (11), 5169-5180 (2011-11)","raw_type":"peer reviewed"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320322644","display_name":"University of Crete","ror":"https://ror.org/00dr28g20"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":44,"referenced_works":["https://openalex.org/W300594107","https://openalex.org/W391578156","https://openalex.org/W1500551892","https://openalex.org/W1503221585","https://openalex.org/W1543525853","https://openalex.org/W1548334834","https://openalex.org/W1568307856","https://openalex.org/W1632601927","https://openalex.org/W1963888335","https://openalex.org/W1981745143","https://openalex.org/W1985123706","https://openalex.org/W1995285162","https://openalex.org/W2033839136","https://openalex.org/W2048679451","https://openalex.org/W2070847953","https://openalex.org/W2078289947","https://openalex.org/W2078979423","https://openalex.org/W2080208950","https://openalex.org/W2089105401","https://openalex.org/W2100440346","https://openalex.org/W2118388189","https://openalex.org/W2119347354","https://openalex.org/W2128202699","https://openalex.org/W2129429798","https://openalex.org/W2134376819","https://openalex.org/W2144931885","https://openalex.org/W2149094052","https://openalex.org/W2149963542","https://openalex.org/W2156202420","https://openalex.org/W2156816269","https://openalex.org/W2159875827","https://openalex.org/W2165775468","https://openalex.org/W2174883827","https://openalex.org/W2266816739","https://openalex.org/W2296319761","https://openalex.org/W2467020497","https://openalex.org/W2610857016","https://openalex.org/W4239749705","https://openalex.org/W4250589301","https://openalex.org/W4253347690","https://openalex.org/W4293860921","https://openalex.org/W6610704622","https://openalex.org/W6632342153","https://openalex.org/W6679439748"],"related_works":["https://openalex.org/W1986006778","https://openalex.org/W2005485125","https://openalex.org/W2390718407","https://openalex.org/W2085363807","https://openalex.org/W2034124193","https://openalex.org/W2379017606","https://openalex.org/W2941765012","https://openalex.org/W2171970890","https://openalex.org/W323147296","https://openalex.org/W38661524"],"abstract_inverted_index":{"The":[0,132,222],"problem":[1,134,220],"of":[2,17,41,57,73,104,148,189,193,224],"finding":[3],"the":[4,45,71,78,88,101,108,149,165,169,187,190,194,217,225],"least":[5,67],"squares":[6],"solution":[7],"<formula":[8,19,31,48,91,110],"formulatype=\"inline\"":[9,20,32,49,92,111],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[10,21,33,50,93,112],"xmlns:xlink=\"http://www.w3.org/1999/xlink\"><tex":[11,22,51,94],"Notation=\"TeX\">${\\bf":[12,23,36,52,95,115],"s}$</tex></formula>":[13,37],"to":[14,61,64,80,87,119,139,179,216],"a":[15,39,74,121,128,145,181],"system":[16],"equations":[18],"Hs}":[24],"=":[25],"{\\bf":[26],"y}$</tex></formula>":[27],"is":[28,38,54,117,135,177,229],"considered,":[29],"when":[30],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">":[34,113],"<tex":[35,114],"vector":[40],"binary":[42,66],"variables":[43],"and":[44,196],"coefficient":[46,170],"matrix":[47,109],"H}$</tex></formula>":[53,96,116],"unknown":[55,123],"but":[56],"bounded":[58],"uncertainty.":[59],"Similar":[60],"previous":[62],"approaches":[63],"robust":[65],"squares,":[68],"we":[69,152,173],"explore":[70],"potential":[72],"min-max":[75],"design":[76],"with":[77],"aim":[79],"provide":[81],"solutions":[82],"that":[83,161,175,201],"are":[84,209],"less":[85],"sensitive":[86],"uncertainty":[89,130,167],"in":[90,127,168,204],".":[97],"We":[98],"concentrate":[99],"on":[100,158],"important":[102],"case":[103],"ellipsoidal":[105,166],"uncertainty,":[106],"i.e.,":[107],"assumed":[118],"be":[120],"deterministic":[122],"quantity":[124],"which":[125],"lies":[126],"given":[129],"ellipsoid.":[131],"resulting":[133],"NP-hard,":[136],"yet":[137],"amenable":[138],"convex":[140],"approximation":[141,155,199],"techniques:":[142],"Starting":[143],"from":[144],"convenient":[146],"reformulation":[147],"original":[150],"problem,":[151,195],"propose":[153],"an":[154,198],"algorithm":[156,200],"based":[157],"semidefinite":[159],"relaxation":[160,183,228],"explicitly":[162],"accounts":[163],"for":[164],"matrix.":[171],"Next,":[172],"show":[174],"it":[176],"possible":[178],"construct":[180],"tighter":[182],"by":[184,231],"suitably":[185],"changing":[186],"description":[188],"feasible":[191],"region":[192],"formulate":[197],"performs":[202],"better":[203],"practice.":[205],"Interestingly,":[206],"both":[207],"relaxations":[208],"derived":[210],"as":[211],"Lagrange":[212],"bidual":[213],"problems":[214],"corresponding":[215],"two":[218],"equivalent":[219],"reformulations.":[221],"strength":[223],"proposed":[226],"tightened":[227],"demonstrated":[230],"pertinent":[232],"simulations.":[233]},"counts_by_year":[{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
