{"id":"https://openalex.org/W7123369823","doi":"https://doi.org/10.1109/cdc57313.2025.11312566","title":"Semidefinite Programming Duality in Infinite-Horizon Linear Quadratic Differential Games","display_name":"Semidefinite Programming Duality in Infinite-Horizon Linear Quadratic Differential Games","publication_year":2025,"publication_date":"2025-12-09","ids":{"openalex":"https://openalex.org/W7123369823","doi":"https://doi.org/10.1109/cdc57313.2025.11312566"},"language":null,"primary_location":{"id":"doi:10.1109/cdc57313.2025.11312566","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc57313.2025.11312566","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2025 IEEE 64th Conference on Decision and Control (CDC)","raw_type":"proceedings-article"},"type":"conference-paper","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/A5101026405","display_name":"Yuto Watanabe","orcid":"https://orcid.org/0009-0003-4035-8154"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Yuto Watanabe","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5102598004","display_name":"Chih-fan Pai","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Chih-Fan Pai","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5122905817","display_name":"Yang Zheng","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Yang Zheng","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.5254,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.91683708,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":91,"max":95},"biblio":{"volume":null,"issue":null,"first_page":"3964","last_page":"3970"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10545","display_name":"Optimization and Variational Analysis","score":0.37450000643730164,"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"}},"topics":[{"id":"https://openalex.org/T10545","display_name":"Optimization and Variational Analysis","score":0.37450000643730164,"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/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.28200000524520874,"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/T11612","display_name":"Stochastic Gradient Optimization Techniques","score":0.06939999759197235,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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":0.7953000068664551},{"id":"https://openalex.org/keywords/convex-optimization","display_name":"Convex optimization","score":0.5656999945640564},{"id":"https://openalex.org/keywords/duality","display_name":"Duality (order theory)","score":0.5625},{"id":"https://openalex.org/keywords/semidefinite-embedding","display_name":"Semidefinite embedding","score":0.47350001335144043},{"id":"https://openalex.org/keywords/optimal-control","display_name":"Optimal control","score":0.4675000011920929},{"id":"https://openalex.org/keywords/linear-matrix-inequality","display_name":"Linear matrix inequality","score":0.45750001072883606},{"id":"https://openalex.org/keywords/mathematical-proof","display_name":"Mathematical proof","score":0.42170000076293945},{"id":"https://openalex.org/keywords/saddle-point","display_name":"Saddle point","score":0.41990000009536743},{"id":"https://openalex.org/keywords/leverage","display_name":"Leverage (statistics)","score":0.4083000123500824},{"id":"https://openalex.org/keywords/second-order-cone-programming","display_name":"Second-order cone programming","score":0.4043999910354614}],"concepts":[{"id":"https://openalex.org/C101901036","wikidata":"https://www.wikidata.org/wiki/Q2269096","display_name":"Semidefinite programming","level":2,"score":0.7953000068664551},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6912000179290771},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.5656999945640564},{"id":"https://openalex.org/C2778023678","wikidata":"https://www.wikidata.org/wiki/Q554403","display_name":"Duality (order theory)","level":2,"score":0.5625},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.49709999561309814},{"id":"https://openalex.org/C206818286","wikidata":"https://www.wikidata.org/wiki/Q7449403","display_name":"Semidefinite embedding","level":4,"score":0.47350001335144043},{"id":"https://openalex.org/C91575142","wikidata":"https://www.wikidata.org/wiki/Q1971426","display_name":"Optimal control","level":2,"score":0.4675000011920929},{"id":"https://openalex.org/C201829737","wikidata":"https://www.wikidata.org/wiki/Q2022760","display_name":"Linear matrix inequality","level":2,"score":0.45750001072883606},{"id":"https://openalex.org/C108710211","wikidata":"https://www.wikidata.org/wiki/Q11538","display_name":"Mathematical proof","level":2,"score":0.42170000076293945},{"id":"https://openalex.org/C2681867","wikidata":"https://www.wikidata.org/wiki/Q690935","display_name":"Saddle point","level":2,"score":0.41990000009536743},{"id":"https://openalex.org/C153083717","wikidata":"https://www.wikidata.org/wiki/Q6535263","display_name":"Leverage (statistics)","level":2,"score":0.4083000123500824},{"id":"https://openalex.org/C111397411","wikidata":"https://www.wikidata.org/wiki/Q7442977","display_name":"Second-order cone programming","level":4,"score":0.4043999910354614},{"id":"https://openalex.org/C81845259","wikidata":"https://www.wikidata.org/wiki/Q290117","display_name":"Quadratic programming","level":2,"score":0.40369999408721924},{"id":"https://openalex.org/C41045048","wikidata":"https://www.wikidata.org/wiki/Q202843","display_name":"Linear programming","level":2,"score":0.4034000039100647},{"id":"https://openalex.org/C65148998","wikidata":"https://www.wikidata.org/wiki/Q7268373","display_name":"Quadratically constrained quadratic program","level":3,"score":0.4025999903678894},{"id":"https://openalex.org/C77246614","wikidata":"https://www.wikidata.org/wiki/Q1409400","display_name":"Gramian matrix","level":3,"score":0.39969998598098755},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.3921000063419342},{"id":"https://openalex.org/C5274546","wikidata":"https://www.wikidata.org/wiki/Q5310264","display_name":"Duality gap","level":3,"score":0.3815000057220459},{"id":"https://openalex.org/C12108790","wikidata":"https://www.wikidata.org/wiki/Q2234833","display_name":"Convex analysis","level":4,"score":0.37869998812675476},{"id":"https://openalex.org/C2779006483","wikidata":"https://www.wikidata.org/wiki/Q1973196","display_name":"Differential game","level":2,"score":0.36980000138282776},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.35740000009536743},{"id":"https://openalex.org/C177142836","wikidata":"https://www.wikidata.org/wiki/Q44455","display_name":"Game theory","level":2,"score":0.35260000824928284},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.3492000102996826},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.3467000126838684},{"id":"https://openalex.org/C93226319","wikidata":"https://www.wikidata.org/wiki/Q193137","display_name":"Differential (mechanical device)","level":2,"score":0.3422999978065491},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3379000127315521},{"id":"https://openalex.org/C31531917","wikidata":"https://www.wikidata.org/wiki/Q915157","display_name":"Robust control","level":3,"score":0.3303999900817871},{"id":"https://openalex.org/C94940","wikidata":"https://www.wikidata.org/wiki/Q652941","display_name":"Hermitian matrix","level":2,"score":0.32510000467300415},{"id":"https://openalex.org/C163863214","wikidata":"https://www.wikidata.org/wiki/Q7624553","display_name":"Strong duality","level":3,"score":0.31520000100135803},{"id":"https://openalex.org/C155253501","wikidata":"https://www.wikidata.org/wiki/Q461992","display_name":"Interior point method","level":2,"score":0.3077000081539154},{"id":"https://openalex.org/C2780012671","wikidata":"https://www.wikidata.org/wiki/Q1343870","display_name":"Corollary","level":2,"score":0.3075999915599823},{"id":"https://openalex.org/C92207270","wikidata":"https://www.wikidata.org/wiki/Q939253","display_name":"Matrix norm","level":3,"score":0.30489999055862427},{"id":"https://openalex.org/C79187972","wikidata":"https://www.wikidata.org/wiki/Q2654791","display_name":"Conic optimization","level":5,"score":0.301800012588501},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.2964000105857849},{"id":"https://openalex.org/C145446738","wikidata":"https://www.wikidata.org/wiki/Q319913","display_name":"Convex function","level":3,"score":0.29109999537467957},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.2879999876022339},{"id":"https://openalex.org/C80682859","wikidata":"https://www.wikidata.org/wiki/Q7977943","display_name":"Weak duality","level":4,"score":0.28279998898506165},{"id":"https://openalex.org/C2777127463","wikidata":"https://www.wikidata.org/wiki/Q10862618","display_name":"Saddle","level":2,"score":0.25929999351501465},{"id":"https://openalex.org/C49712288","wikidata":"https://www.wikidata.org/wiki/Q77601250","display_name":"Positive-definite matrix","level":3,"score":0.2581000030040741},{"id":"https://openalex.org/C117312493","wikidata":"https://www.wikidata.org/wiki/Q2035437","display_name":"Multivariable calculus","level":2,"score":0.25440001487731934}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/cdc57313.2025.11312566","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc57313.2025.11312566","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2025 IEEE 64th Conference on Decision and Control (CDC)","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":17,"referenced_works":["https://openalex.org/W1894079357","https://openalex.org/W2002357820","https://openalex.org/W2039867272","https://openalex.org/W2080509449","https://openalex.org/W2115424783","https://openalex.org/W2115832833","https://openalex.org/W2304905162","https://openalex.org/W2498694880","https://openalex.org/W2912522929","https://openalex.org/W3128710479","https://openalex.org/W3210839039","https://openalex.org/W4225795442","https://openalex.org/W4367841446","https://openalex.org/W4388319978","https://openalex.org/W4403768163","https://openalex.org/W4409639154","https://openalex.org/W7123369823"],"related_works":[],"abstract_inverted_index":{"Semidefinite":[0],"programs":[1],"(SDPs)":[2],"play":[3],"a":[4,12,62],"crucial":[5],"role":[6],"in":[7,20,34,54,77],"control":[8,93,110,132,136],"theory,":[9],"traditionally":[10],"as":[11],"computational":[13],"tool.":[14],"Beyond":[15],"computation,":[16],"the":[17,48,69,84,106,118,126],"duality":[18],"theory":[19],"convex":[21,97],"optimization":[22],"also":[23,100],"provides":[24,117],"valuable":[25],"analytical":[26,42],"insights":[27],"and":[28,129,137],"new":[29,63],"proofs":[30],"of":[31,44],"classical":[32],"results":[33],"control.":[35],"In":[36],"this":[37,41,102,115],"work,":[38],"we":[39,60,82],"extend":[40,101],"use":[43],"SDPs":[45],"to":[46,67,105],"study":[47],"infinite-horizon":[49],"linear-quadratic":[50],"(LQ)":[51],"differential":[52],"game":[53,128],"continuous":[55],"time.":[56],"Under":[57],"standard":[58],"assumptions,":[59],"introduce":[61],"SDP-based":[64],"primal-dual":[65,120],"approach":[66],"establish":[68],"saddle":[70],"point":[71],"characterized":[72],"by":[73],"linear":[74,91],"static":[75],"policies":[76],"LQ":[78,127,134],"games.":[79],"For":[80],"this,":[81],"leverage":[83],"Gramian":[85,123],"representation":[86],"technique,":[87],"which":[88],"elegantly":[89],"transforms":[90],"quadratic":[92],"problems":[94],"into":[95],"tractable":[96],"programs.":[98],"We":[99],"duality-based":[103],"proof":[104],"${{\\mathcal{H}}_\\infty":[107,130,138],"}$":[108,131,139],"suboptimal":[109],"problem.":[111],"To":[112],"our":[113],"knowledge,":[114],"work":[116],"first":[119],"analysis":[121],"using":[122],"representations":[124],"for":[125],"beyond":[133],"optimal":[135],"analysis.":[140]},"counts_by_year":[{"year":2025,"cited_by_count":1}],"updated_date":"2026-07-29T14:22:42.915294","created_date":"2026-01-14T00:00:00"}