{"id":"https://openalex.org/W4391021275","doi":"https://doi.org/10.1109/cdc49753.2023.10383895","title":"A Spectral Bundle Method for Sparse Semidefinite Programs","display_name":"A Spectral Bundle Method for Sparse Semidefinite Programs","publication_year":2023,"publication_date":"2023-12-13","ids":{"openalex":"https://openalex.org/W4391021275","doi":"https://doi.org/10.1109/cdc49753.2023.10383895"},"language":"en","primary_location":{"id":"doi:10.1109/cdc49753.2023.10383895","is_oa":false,"landing_page_url":"http://dx.doi.org/10.1109/cdc49753.2023.10383895","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2023 62nd IEEE Conference on Decision and Control (CDC)","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/A5055047664","display_name":"Hesam Mojtahedi","orcid":null},"institutions":[{"id":"https://openalex.org/I36258959","display_name":"University of California, San Diego","ror":"https://ror.org/0168r3w48","country_code":"US","type":"education","lineage":["https://openalex.org/I36258959"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Hesam Mojtahedi","raw_affiliation_strings":["University of California San Diego,Department of Electrical and Computer Engineering,La Jolla,CA,USA,92093"],"affiliations":[{"raw_affiliation_string":"University of California San Diego,Department of Electrical and Computer Engineering,La Jolla,CA,USA,92093","institution_ids":["https://openalex.org/I36258959"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5038386596","display_name":"Feng-Yi Liao","orcid":null},"institutions":[{"id":"https://openalex.org/I36258959","display_name":"University of California, San Diego","ror":"https://ror.org/0168r3w48","country_code":"US","type":"education","lineage":["https://openalex.org/I36258959"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Feng-Yi Liao","raw_affiliation_strings":["University of California San Diego,Department of Electrical and Computer Engineering,La Jolla,CA,USA,92093"],"affiliations":[{"raw_affiliation_string":"University of California San Diego,Department of Electrical and Computer Engineering,La Jolla,CA,USA,92093","institution_ids":["https://openalex.org/I36258959"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5101688327","display_name":"Yang Zheng","orcid":"https://orcid.org/0000-0001-6500-8423"},"institutions":[{"id":"https://openalex.org/I36258959","display_name":"University of California, San Diego","ror":"https://ror.org/0168r3w48","country_code":"US","type":"education","lineage":["https://openalex.org/I36258959"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Yang Zheng","raw_affiliation_strings":["University of California San Diego,Department of Electrical and Computer Engineering,La Jolla,CA,USA,92093"],"affiliations":[{"raw_affiliation_string":"University of California San Diego,Department of Electrical and Computer Engineering,La Jolla,CA,USA,92093","institution_ids":["https://openalex.org/I36258959"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5055047664"],"corresponding_institution_ids":["https://openalex.org/I36258959"],"apc_list":null,"apc_paid":null,"fwci":0.4119,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.60221421,"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":"8254","last_page":"8259"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9997000098228455,"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":0.9997000098228455,"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/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9995999932289124,"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/T10545","display_name":"Optimization and Variational Analysis","score":0.9927999973297119,"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/semidefinite-programming","display_name":"Semidefinite programming","score":0.7070611119270325},{"id":"https://openalex.org/keywords/sublinear-function","display_name":"Sublinear function","score":0.563774585723877},{"id":"https://openalex.org/keywords/bundle","display_name":"Bundle","score":0.5349245071411133},{"id":"https://openalex.org/keywords/subgradient-method","display_name":"Subgradient method","score":0.490922749042511},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.4786164164543152},{"id":"https://openalex.org/keywords/scalability","display_name":"Scalability","score":0.4691307246685028},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.45690053701400757},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.4130493402481079},{"id":"https://openalex.org/keywords/constraint","display_name":"Constraint (computer-aided design)","score":0.41276177763938904},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3978918194770813},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3802351653575897},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3099536895751953}],"concepts":[{"id":"https://openalex.org/C101901036","wikidata":"https://www.wikidata.org/wiki/Q2269096","display_name":"Semidefinite programming","level":2,"score":0.7070611119270325},{"id":"https://openalex.org/C117160843","wikidata":"https://www.wikidata.org/wiki/Q338652","display_name":"Sublinear function","level":2,"score":0.563774585723877},{"id":"https://openalex.org/C2778134712","wikidata":"https://www.wikidata.org/wiki/Q1047307","display_name":"Bundle","level":2,"score":0.5349245071411133},{"id":"https://openalex.org/C158968445","wikidata":"https://www.wikidata.org/wiki/Q7631150","display_name":"Subgradient method","level":2,"score":0.490922749042511},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4786164164543152},{"id":"https://openalex.org/C48044578","wikidata":"https://www.wikidata.org/wiki/Q727490","display_name":"Scalability","level":2,"score":0.4691307246685028},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.45690053701400757},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.4130493402481079},{"id":"https://openalex.org/C2776036281","wikidata":"https://www.wikidata.org/wiki/Q48769818","display_name":"Constraint (computer-aided design)","level":2,"score":0.41276177763938904},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3978918194770813},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3802351653575897},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3099536895751953},{"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/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0},{"id":"https://openalex.org/C77088390","wikidata":"https://www.wikidata.org/wiki/Q8513","display_name":"Database","level":1,"score":0.0},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","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/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/cdc49753.2023.10383895","is_oa":false,"landing_page_url":"http://dx.doi.org/10.1109/cdc49753.2023.10383895","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2023 62nd IEEE Conference on Decision and Control (CDC)","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2557920077","display_name":null,"funder_award_id":"ECCS-2154650,CMMI-2320697","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":27,"referenced_works":["https://openalex.org/W200276062","https://openalex.org/W1963753244","https://openalex.org/W1967073510","https://openalex.org/W1985123706","https://openalex.org/W2014495508","https://openalex.org/W2034769312","https://openalex.org/W2051306216","https://openalex.org/W2071143636","https://openalex.org/W2288174618","https://openalex.org/W2738121580","https://openalex.org/W2912522929","https://openalex.org/W2963774730","https://openalex.org/W2964239200","https://openalex.org/W2968427464","https://openalex.org/W2991461359","https://openalex.org/W2997964792","https://openalex.org/W3044411208","https://openalex.org/W3100916622","https://openalex.org/W3162304593","https://openalex.org/W3205478315","https://openalex.org/W3210839039","https://openalex.org/W4252937232","https://openalex.org/W4292070118","https://openalex.org/W4382065240","https://openalex.org/W4384652346","https://openalex.org/W4391021275","https://openalex.org/W6854890332"],"related_works":["https://openalex.org/W2359120930","https://openalex.org/W2037613239","https://openalex.org/W2781777036","https://openalex.org/W2390469630","https://openalex.org/W2059050877","https://openalex.org/W1971290991","https://openalex.org/W1944783162","https://openalex.org/W4378770495","https://openalex.org/W4361865857","https://openalex.org/W2962762987"],"abstract_inverted_index":{"Semidefinite":[0],"programs":[1],"(SDPs)":[2],"have":[3],"many":[4],"applications":[5],"in":[6,117],"the":[7,19,66,70,132,136,143,158],"field":[8],"of":[9,59,119,138],"controls.":[10],"To":[11],"improve":[12],"scalability,":[13],"it":[14],"is":[15,102],"important":[16],"to":[17,48,78,104,146],"exploit":[18],"inherent":[20],"sparsity":[21],"when":[22,150],"solving":[23],"SDPs.":[24],"In":[25],"this":[26],"paper,":[27],"we":[28,64],"develop":[29],"a":[30,50,57,93,106],"new":[31,94],"spectral":[32,96],"bundle":[33,89,97],"algorithm":[34,133],"that":[35],"solves":[36],"sparse":[37],"SDPs":[38],"without":[39],"introducing":[40],"additional":[41],"variables.":[42],"We":[43,91,112],"first":[44],"apply":[45],"chordal":[46],"decomposition":[47],"replace":[49],"large":[51],"positive":[52],"semidefinite":[53],"(PSD)":[54],"constraint":[55],"with":[56,135],"set":[58],"smaller":[60],"coupled":[61,67],"constraints.":[62],"Then,":[63],"move":[65],"constraints":[68],"into":[69],"cost":[71],"function":[72],"via":[73],"exact":[74],"penalty.":[75],"This":[76],"leads":[77],"an":[79],"equivalent":[80],"non-smooth":[81],"penalized":[82],"problem,":[83],"which":[84],"can":[85],"be":[86],"solved":[87],"by":[88],"methods.":[90],"present":[92],"efficient":[95],"algorithm,":[98],"where":[99],"subgradient":[100],"information":[101],"incorporated":[103],"update":[105],"lower":[107],"approximation":[108],"at":[109],"each":[110],"iteration.":[111],"further":[113],"establish":[114],"sublinear":[115],"convergences":[116],"terms":[118],"objective":[120],"value,":[121],"primal":[122],"feasibility,":[123,125],"dual":[124],"and":[126,142],"duality":[127],"gap.":[128],"Under":[129],"Slater's":[130],"condition,":[131],"converges":[134],"rate":[137,144],"<tex":[139,147],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[140,148],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">$\\mathcal{O}(1/\\epsilon^{3})$</tex>,":[141],"improves":[145],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">$\\mathcal{O}(1/\\epsilon)$</tex>":[149],"strict":[151],"complementarity":[152],"holds.":[153],"Our":[154],"numerical":[155],"experiments":[156],"support":[157],"theoretical":[159],"analysis.":[160]},"counts_by_year":[{"year":2023,"cited_by_count":1}],"updated_date":"2025-12-25T23:11:45.687758","created_date":"2025-10-10T00:00:00"}
