{"id":"https://openalex.org/W2776923082","doi":"https://doi.org/10.1109/ccta.2018.8511584","title":"A Primal-Dual Method for Optimal Control and Trajectory Generation in High-Dimensional Systems","display_name":"A Primal-Dual Method for Optimal Control and Trajectory Generation in High-Dimensional Systems","publication_year":2018,"publication_date":"2018-08-01","ids":{"openalex":"https://openalex.org/W2776923082","doi":"https://doi.org/10.1109/ccta.2018.8511584","mag":"2776923082"},"language":"en","primary_location":{"id":"doi:10.1109/ccta.2018.8511584","is_oa":false,"landing_page_url":"https://doi.org/10.1109/ccta.2018.8511584","pdf_url":null,"source":{"id":"https://openalex.org/S4306498315","display_name":"2018 IEEE Conference on Control Technology and Applications (CCTA)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"conference"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2018 IEEE Conference on Control Technology and Applications (CCTA)","raw_type":"proceedings-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1712.08226","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Matthew R. Kirchner","orcid":null},"institutions":[{"id":"https://openalex.org/I4210121626","display_name":"Signal Processing (United States)","ror":"https://ror.org/021gzyw51","country_code":"US","type":"company","lineage":["https://openalex.org/I4210121626"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Matthew R. Kirchner","raw_affiliation_strings":["Image and Signal Processing Branch, Research Directorate, China Lake, CA, USA"],"affiliations":[{"raw_affiliation_string":"Image and Signal Processing Branch, Research Directorate, China Lake, CA, USA","institution_ids":["https://openalex.org/I4210121626"]}]},{"author_position":"middle","author":{"id":null,"display_name":"Gary Hewer","orcid":null},"institutions":[{"id":"https://openalex.org/I4210121626","display_name":"Signal Processing (United States)","ror":"https://ror.org/021gzyw51","country_code":"US","type":"company","lineage":["https://openalex.org/I4210121626"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Gary Hewer","raw_affiliation_strings":["Image and Signal Processing Branch, Research Directorate, China Lake, CA, USA"],"affiliations":[{"raw_affiliation_string":"Image and Signal Processing Branch, Research Directorate, China Lake, CA, USA","institution_ids":["https://openalex.org/I4210121626"]}]},{"author_position":"middle","author":{"id":null,"display_name":"Jerome Darbon","orcid":null},"institutions":[{"id":"https://openalex.org/I27804330","display_name":"Brown University","ror":"https://ror.org/05gq02987","country_code":"US","type":"education","lineage":["https://openalex.org/I27804330"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Jerome Darbon","raw_affiliation_strings":["Division of Applied Mathematics, Brown Univer-sitv, Providence, RI, USA"],"affiliations":[{"raw_affiliation_string":"Division of Applied Mathematics, Brown Univer-sitv, Providence, RI, USA","institution_ids":["https://openalex.org/I27804330"]}]},{"author_position":"last","author":{"id":null,"display_name":"Stanley Osher","orcid":null},"institutions":[{"id":"https://openalex.org/I161318765","display_name":"University of California, Los Angeles","ror":"https://ror.org/046rm7j60","country_code":"US","type":"education","lineage":["https://openalex.org/I161318765"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Stanley Osher","raw_affiliation_strings":["Department of Mathematics, University of California, Los Angeles, CA, USA"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of California, Los Angeles, CA, USA","institution_ids":["https://openalex.org/I161318765"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I4210121626"],"apc_list":null,"apc_paid":null,"fwci":5.0776,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":{"value":0.93281464,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"12","issue":null,"first_page":"1583","last_page":"1590"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11082","display_name":"Spacecraft Dynamics and Control","score":0.6843000054359436,"subfield":{"id":"https://openalex.org/subfields/2202","display_name":"Aerospace 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/T11082","display_name":"Spacecraft Dynamics and Control","score":0.6843000054359436,"subfield":{"id":"https://openalex.org/subfields/2202","display_name":"Aerospace 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/T10545","display_name":"Optimization and Variational Analysis","score":0.16840000450611115,"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/T11416","display_name":"Numerical methods for differential equations","score":0.023399999365210533,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/optimal-control","display_name":"Optimal control","score":0.5942000150680542},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.5723000168800354},{"id":"https://openalex.org/keywords/trajectory","display_name":"Trajectory","score":0.5187000036239624},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.5098999738693237},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.48730000853538513},{"id":"https://openalex.org/keywords/grid","display_name":"Grid","score":0.43470001220703125},{"id":"https://openalex.org/keywords/exponential-function","display_name":"Exponential function","score":0.38280001282691956},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.33709999918937683}],"concepts":[{"id":"https://openalex.org/C91575142","wikidata":"https://www.wikidata.org/wiki/Q1971426","display_name":"Optimal control","level":2,"score":0.5942000150680542},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5910000205039978},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.5723000168800354},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5472000241279602},{"id":"https://openalex.org/C13662910","wikidata":"https://www.wikidata.org/wiki/Q193139","display_name":"Trajectory","level":2,"score":0.5187000036239624},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.5098999738693237},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.48730000853538513},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4690000116825104},{"id":"https://openalex.org/C187691185","wikidata":"https://www.wikidata.org/wiki/Q2020720","display_name":"Grid","level":2,"score":0.43470001220703125},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.38280001282691956},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.33709999918937683},{"id":"https://openalex.org/C99844830","wikidata":"https://www.wikidata.org/wiki/Q102441924","display_name":"Scaling","level":2,"score":0.32690000534057617},{"id":"https://openalex.org/C18762648","wikidata":"https://www.wikidata.org/wiki/Q42213","display_name":"Work (physics)","level":2,"score":0.32350000739097595},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.32350000739097595},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3228999972343445},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.29269999265670776},{"id":"https://openalex.org/C173246807","wikidata":"https://www.wikidata.org/wiki/Q7833062","display_name":"Trajectory optimization","level":3,"score":0.29100000858306885},{"id":"https://openalex.org/C2778755073","wikidata":"https://www.wikidata.org/wiki/Q10858537","display_name":"Scale (ratio)","level":2,"score":0.29019999504089355},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.2881999909877777},{"id":"https://openalex.org/C137800194","wikidata":"https://www.wikidata.org/wiki/Q11713455","display_name":"Interpolation (computer graphics)","level":3,"score":0.28529998660087585},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.2847999930381775},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.26429998874664307},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.25780001282691956},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.25360000133514404},{"id":"https://openalex.org/C26955809","wikidata":"https://www.wikidata.org/wiki/Q10167591","display_name":"Initial value problem","level":2,"score":0.2515000104904175}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/ccta.2018.8511584","is_oa":false,"landing_page_url":"https://doi.org/10.1109/ccta.2018.8511584","pdf_url":null,"source":{"id":"https://openalex.org/S4306498315","display_name":"2018 IEEE Conference on Control Technology and Applications (CCTA)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"conference"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2018 IEEE Conference on Control Technology and Applications (CCTA)","raw_type":"proceedings-article"},{"id":"pmh:oai:arXiv.org:1712.08226","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1712.08226","pdf_url":"https://arxiv.org/pdf/1712.08226","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1712.08226","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1712.08226","pdf_url":"https://arxiv.org/pdf/1712.08226","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":23,"referenced_works":["https://openalex.org/W1946620893","https://openalex.org/W2001331101","https://openalex.org/W2026570525","https://openalex.org/W2028212620","https://openalex.org/W2050188930","https://openalex.org/W2092663520","https://openalex.org/W2107802551","https://openalex.org/W2116364955","https://openalex.org/W2123487311","https://openalex.org/W2142058898","https://openalex.org/W2158449358","https://openalex.org/W2239043582","https://openalex.org/W2294813034","https://openalex.org/W2503277810","https://openalex.org/W2505474855","https://openalex.org/W2759865216","https://openalex.org/W2963395620","https://openalex.org/W4244393449","https://openalex.org/W6606935068","https://openalex.org/W6634785237","https://openalex.org/W6690752038","https://openalex.org/W6722495385","https://openalex.org/W6736999073"],"related_works":[],"abstract_inverted_index":{"Presented":[0],"is":[1,68],"a":[2,31,73,87],"method":[3,89],"for":[4,12,90],"efficient":[5,91],"computation":[6,128],"of":[7,34,51,108,123],"the":[8,17,26,35,49,97,106,109,121],"Hamilton-Jacobi":[9],"(HJ)":[10],"equation":[11,28],"time-optimal":[13],"control":[14],"problems":[15],"using":[16],"generalized":[18,45],"Hopf":[19,46,110],"formula.":[20],"Typically,":[21],"numerical":[22,54],"methods":[23],"to":[24],"solve":[25],"HJ":[27],"rely":[29],"on":[30,120],"discrete":[32],"grid":[33],"solution":[36,64,93,107],"space":[37],"and":[38,53,71,94,125],"exhibit":[39],"exponential":[40],"scaling":[41],"with":[42,134],"dimension.":[43],"The":[44,63],"formula":[47],"avoids":[48],"use":[50],"grids":[52],"gradients":[55],"by":[56],"formulating":[57],"an":[58],"unconstrained":[59],"convex":[60],"optimization":[61],"problem.":[62],"at":[65,79],"each":[66],"point":[67],"completely":[69],"independent,":[70],"allows":[72],"massively":[74],"parallel":[75],"implementation":[76],"if":[77],"solutions":[78],"multiple":[80],"points":[81],"are":[82],"desired.":[83],"This":[84],"work":[85],"presents":[86,95],"primal-dual":[88],"numeric":[92],"how":[96],"resulting":[98],"optimal":[99],"trajectory":[100],"can":[101],"be":[102],"generated":[103],"directly":[104],"from":[105],"formula,":[111],"without":[112],"further":[113],"optimization.":[114],"Examples":[115],"presented":[116],"have":[117],"execution":[118],"times":[119],"order":[122],"milliseconds":[124],"experiments":[126],"show":[127],"scales":[129],"approximately":[130],"polynomial":[131],"in":[132],"dimension":[133],"very":[135],"small":[136],"high-order":[137],"coefficients.":[138]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":1}],"updated_date":"2026-03-10T16:38:18.471706","created_date":"2018-01-05T00:00:00"}
