{"id":"https://openalex.org/W2016090484","doi":"https://doi.org/10.1109/acc.2012.6315611","title":"An Ellipsoid Algorithm for linear optimization with uncertain LMI constraints","display_name":"An Ellipsoid Algorithm for linear optimization with uncertain LMI constraints","publication_year":2012,"publication_date":"2012-06-01","ids":{"openalex":"https://openalex.org/W2016090484","doi":"https://doi.org/10.1109/acc.2012.6315611","mag":"2016090484"},"language":"en","primary_location":{"id":"doi:10.1109/acc.2012.6315611","is_oa":false,"landing_page_url":"https://doi.org/10.1109/acc.2012.6315611","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2012 American Control Conference (ACC)","raw_type":"proceedings-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/A5081295930","display_name":"Armin Ataei","orcid":null},"institutions":[{"id":"https://openalex.org/I130769515","display_name":"Pennsylvania State University","ror":"https://ror.org/04p491231","country_code":"US","type":"education","lineage":["https://openalex.org/I130769515"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"A. Ataei","raw_affiliation_strings":["Department of Mechanical and Nuclear Engineering, Pennsylvania State University, USA","Department of Mechanical and Nuclear Engineering, The Pennsylvania State University"],"affiliations":[{"raw_affiliation_string":"Department of Mechanical and Nuclear Engineering, Pennsylvania State University, USA","institution_ids":["https://openalex.org/I130769515"]},{"raw_affiliation_string":"Department of Mechanical and Nuclear Engineering, The Pennsylvania State University","institution_ids":["https://openalex.org/I130769515"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100743351","display_name":"Qian Wang","orcid":"https://orcid.org/0000-0001-7159-1424"},"institutions":[{"id":"https://openalex.org/I130769515","display_name":"Pennsylvania State University","ror":"https://ror.org/04p491231","country_code":"US","type":"education","lineage":["https://openalex.org/I130769515"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Qian Wang","raw_affiliation_strings":["Department of Mechanical and Nuclear Engineering, Pennsylvania State University, USA","Department of Mechanical and Nuclear Engineering, The Pennsylvania State University"],"affiliations":[{"raw_affiliation_string":"Department of Mechanical and Nuclear Engineering, Pennsylvania State University, USA","institution_ids":["https://openalex.org/I130769515"]},{"raw_affiliation_string":"Department of Mechanical and Nuclear Engineering, The Pennsylvania State University","institution_ids":["https://openalex.org/I130769515"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5081295930"],"corresponding_institution_ids":["https://openalex.org/I130769515"],"apc_list":null,"apc_paid":null,"fwci":0.9014,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.72486655,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9991999864578247,"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":0.9991999864578247,"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":0.9979000091552734,"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/T10545","display_name":"Optimization and Variational Analysis","score":0.9939000010490417,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/ellipsoid","display_name":"Ellipsoid","score":0.9409278631210327},{"id":"https://openalex.org/keywords/ellipsoid-method","display_name":"Ellipsoid method","score":0.8650485277175903},{"id":"https://openalex.org/keywords/probabilistic-logic","display_name":"Probabilistic logic","score":0.6650097370147705},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.5902778506278992},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5872042775154114},{"id":"https://openalex.org/keywords/linear-matrix-inequality","display_name":"Linear matrix inequality","score":0.541711688041687},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5211629867553711},{"id":"https://openalex.org/keywords/feasible-region","display_name":"Feasible region","score":0.5152866840362549},{"id":"https://openalex.org/keywords/linear-programming","display_name":"Linear programming","score":0.4700537919998169},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4573246240615845},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.4564116597175598},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.42306599020957947},{"id":"https://openalex.org/keywords/linear-system","display_name":"Linear system","score":0.4185207486152649},{"id":"https://openalex.org/keywords/optimization-problem","display_name":"Optimization problem","score":0.4155004620552063},{"id":"https://openalex.org/keywords/convex-optimization","display_name":"Convex optimization","score":0.20585599541664124},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.08904719352722168},{"id":"https://openalex.org/keywords/subderivative","display_name":"Subderivative","score":0.07291674613952637}],"concepts":[{"id":"https://openalex.org/C57489055","wikidata":"https://www.wikidata.org/wiki/Q190046","display_name":"Ellipsoid","level":2,"score":0.9409278631210327},{"id":"https://openalex.org/C205451395","wikidata":"https://www.wikidata.org/wiki/Q378574","display_name":"Ellipsoid method","level":5,"score":0.8650485277175903},{"id":"https://openalex.org/C49937458","wikidata":"https://www.wikidata.org/wiki/Q2599292","display_name":"Probabilistic logic","level":2,"score":0.6650097370147705},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.5902778506278992},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5872042775154114},{"id":"https://openalex.org/C201829737","wikidata":"https://www.wikidata.org/wiki/Q2022760","display_name":"Linear matrix inequality","level":2,"score":0.541711688041687},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5211629867553711},{"id":"https://openalex.org/C177067428","wikidata":"https://www.wikidata.org/wiki/Q17013331","display_name":"Feasible region","level":2,"score":0.5152866840362549},{"id":"https://openalex.org/C41045048","wikidata":"https://www.wikidata.org/wiki/Q202843","display_name":"Linear programming","level":2,"score":0.4700537919998169},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4573246240615845},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.4564116597175598},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.42306599020957947},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.4185207486152649},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.4155004620552063},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.20585599541664124},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.08904719352722168},{"id":"https://openalex.org/C200661725","wikidata":"https://www.wikidata.org/wiki/Q289500","display_name":"Subderivative","level":4,"score":0.07291674613952637},{"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/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C1276947","wikidata":"https://www.wikidata.org/wiki/Q333","display_name":"Astronomy","level":1,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/acc.2012.6315611","is_oa":false,"landing_page_url":"https://doi.org/10.1109/acc.2012.6315611","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2012 American Control Conference (ACC)","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":19,"referenced_works":["https://openalex.org/W1505731132","https://openalex.org/W1539402525","https://openalex.org/W1972546746","https://openalex.org/W2014211039","https://openalex.org/W2050434204","https://openalex.org/W2066698330","https://openalex.org/W2084575717","https://openalex.org/W2102573976","https://openalex.org/W2109439079","https://openalex.org/W2117844706","https://openalex.org/W2123745126","https://openalex.org/W2134815022","https://openalex.org/W2147578396","https://openalex.org/W2167412190","https://openalex.org/W2168251422","https://openalex.org/W2170110056","https://openalex.org/W3210839039","https://openalex.org/W4243448718","https://openalex.org/W4253214256"],"related_works":["https://openalex.org/W2031732959","https://openalex.org/W2235431948","https://openalex.org/W7739709","https://openalex.org/W1500330311","https://openalex.org/W2562629174","https://openalex.org/W2061711344","https://openalex.org/W1966228561","https://openalex.org/W2016090484","https://openalex.org/W2171586366","https://openalex.org/W2189529046"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"an":[3,29],"efficient":[4],"algorithm":[5,48],"based":[6],"on":[7],"the":[8,40,78,85,89],"ellipsoid":[9,47],"method":[10],"is":[11,36,49,81],"proposed":[12,46],"to":[13,51,53,67],"solve":[14],"a":[15,20,54,73],"linear":[16],"optimization":[17],"problem":[18],"over":[19],"set":[21,41,74],"of":[22,42,75,88],"uncertain":[23,43],"Linear":[24],"Matrix":[25],"Inequalities":[26],"(LMIs).":[27],"First,":[28],"Ellipsoid":[30],"Algorithm":[31],"(EA)":[32],"with":[33,58],"deep":[34],"cuts":[35],"introduced":[37],"for":[38],"solving":[39],"LMIs.":[44],"The":[45],"shown":[50],"converge":[52],"probabilistically":[55],"feasible":[56],"point":[57],"high":[59],"confidence":[60],"level":[61],"and":[62],"in":[63],"fewer":[64],"iterations":[65],"compared":[66],"other":[68],"EA":[69],"methods.":[70],"Then,":[71],"through":[72],"new":[76],"cuts,":[77],"objective":[79],"function":[80],"minimized":[82],"while":[83],"maintaining":[84],"probabilistic":[86],"feasibility":[87],"solution.":[90]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2015,"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"}