{"id":"https://openalex.org/W3127025626","doi":"https://doi.org/10.1137/20m1361572","title":"Fine Metrizable Convex Relaxations of Parabolic Optimal Control Problems","display_name":"Fine Metrizable Convex Relaxations of Parabolic Optimal Control Problems","publication_year":2021,"publication_date":"2021-01-01","ids":{"openalex":"https://openalex.org/W3127025626","doi":"https://doi.org/10.1137/20m1361572","mag":"3127025626"},"language":"en","primary_location":{"id":"doi:10.1137/20m1361572","is_oa":false,"landing_page_url":"https://doi.org/10.1137/20m1361572","pdf_url":null,"source":{"id":"https://openalex.org/S897311980","display_name":"SIAM Journal on Control and Optimization","issn_l":"0363-0129","issn":["0363-0129","1095-7138"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Control and Optimization","raw_type":"journal-article"},"type":"preprint","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2102.00254","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5078525963","display_name":"Tom\u00e1\u0161 Roub\u0131\u0301\u010dek","orcid":"https://orcid.org/0000-0002-0651-5959"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Tom\u00e1\u0161 Roub\u00ed\u010dek","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0000-0002-0651-5959","affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5078525963"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.01298521,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"59","issue":"2","first_page":"1293","last_page":"1311"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11110","display_name":"Stability and Controllability of Differential Equations","score":0.9980000257492065,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems 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/T11110","display_name":"Stability and Controllability of Differential Equations","score":0.9980000257492065,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems 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":0.9958000183105469,"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/T10194","display_name":"Nonlinear Partial Differential Equations","score":0.9954000115394592,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/compactification","display_name":"Compactification (mathematics)","score":0.8061943054199219},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7281600832939148},{"id":"https://openalex.org/keywords/metrization-theorem","display_name":"Metrization theorem","score":0.7067263722419739},{"id":"https://openalex.org/keywords/choquet-theory","display_name":"Choquet theory","score":0.6899569630622864},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.6280481219291687},{"id":"https://openalex.org/keywords/optimal-control","display_name":"Optimal control","score":0.5408793687820435},{"id":"https://openalex.org/keywords/convex-analysis","display_name":"Convex analysis","score":0.434656023979187},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4048006236553192},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.38706523180007935},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.378385990858078},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.37004974484443665},{"id":"https://openalex.org/keywords/convex-optimization","display_name":"Convex optimization","score":0.3140244781970978},{"id":"https://openalex.org/keywords/separable-space","display_name":"Separable space","score":0.09237122535705566},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.0789012610912323}],"concepts":[{"id":"https://openalex.org/C2779165322","wikidata":"https://www.wikidata.org/wiki/Q546145","display_name":"Compactification (mathematics)","level":2,"score":0.8061943054199219},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7281600832939148},{"id":"https://openalex.org/C105433845","wikidata":"https://www.wikidata.org/wiki/Q1194053","display_name":"Metrization theorem","level":3,"score":0.7067263722419739},{"id":"https://openalex.org/C176684429","wikidata":"https://www.wikidata.org/wiki/Q1076274","display_name":"Choquet theory","level":5,"score":0.6899569630622864},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.6280481219291687},{"id":"https://openalex.org/C91575142","wikidata":"https://www.wikidata.org/wiki/Q1971426","display_name":"Optimal control","level":2,"score":0.5408793687820435},{"id":"https://openalex.org/C12108790","wikidata":"https://www.wikidata.org/wiki/Q2234833","display_name":"Convex analysis","level":4,"score":0.434656023979187},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4048006236553192},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.38706523180007935},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.378385990858078},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.37004974484443665},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.3140244781970978},{"id":"https://openalex.org/C70710897","wikidata":"https://www.wikidata.org/wiki/Q680081","display_name":"Separable space","level":2,"score":0.09237122535705566},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0789012610912323}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1137/20m1361572","is_oa":false,"landing_page_url":"https://doi.org/10.1137/20m1361572","pdf_url":null,"source":{"id":"https://openalex.org/S897311980","display_name":"SIAM Journal on Control and Optimization","issn_l":"0363-0129","issn":["0363-0129","1095-7138"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Control and Optimization","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:2102.00254","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2102.00254","pdf_url":"https://arxiv.org/pdf/2102.00254","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":"cc-by-nc-sa","license_id":"https://openalex.org/licenses/cc-by-nc-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"text"},{"id":"mag:3127025626","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/2102.00254.pdf","pdf_url":null,"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":"arXiv (Cornell University)","raw_type":null},{"id":"doi:10.48550/arxiv.2102.00254","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2102.00254","pdf_url":null,"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":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2102.00254","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2102.00254","pdf_url":"https://arxiv.org/pdf/2102.00254","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":"cc-by-nc-sa","license_id":"https://openalex.org/licenses/cc-by-nc-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"text"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2091792661","display_name":null,"funder_award_id":"CZ.02.1.01/0.0/0.0/15-003/0000493","funder_id":"https://openalex.org/F4320321005","funder_display_name":"Ministerstvo \u0160kolstv\u00ed, Ml\u00e1de\u017ee a T\u011blov\u00fdchovy"},{"id":"https://openalex.org/G8048287575","display_name":null,"funder_award_id":"19-04956S","funder_id":"https://openalex.org/F4320321006","funder_display_name":"Grantov\u00e1 Agentura \u010cesk\u00e9 Republiky"}],"funders":[{"id":"https://openalex.org/F4320321005","display_name":"Ministerstvo \u0160kolstv\u00ed, Ml\u00e1de\u017ee a T\u011blov\u00fdchovy","ror":"https://ror.org/037n8p820"},{"id":"https://openalex.org/F4320321006","display_name":"Grantov\u00e1 Agentura \u010cesk\u00e9 Republiky","ror":"https://ror.org/01pv73b02"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3127025626.pdf","grobid_xml":"https://content.openalex.org/works/W3127025626.grobid-xml"},"referenced_works_count":32,"referenced_works":["https://openalex.org/W20807139","https://openalex.org/W27423464","https://openalex.org/W262157801","https://openalex.org/W565681979","https://openalex.org/W840789590","https://openalex.org/W1508909650","https://openalex.org/W1511193804","https://openalex.org/W1527702209","https://openalex.org/W1531856058","https://openalex.org/W1539074041","https://openalex.org/W1584259498","https://openalex.org/W1602423691","https://openalex.org/W1986683665","https://openalex.org/W1992510177","https://openalex.org/W1992774846","https://openalex.org/W1997574860","https://openalex.org/W2020412227","https://openalex.org/W2043841940","https://openalex.org/W2054310064","https://openalex.org/W2062035537","https://openalex.org/W2077219618","https://openalex.org/W2077575281","https://openalex.org/W2096391565","https://openalex.org/W2109168354","https://openalex.org/W2168987664","https://openalex.org/W2178676202","https://openalex.org/W2280409710","https://openalex.org/W2317587126","https://openalex.org/W2511035558","https://openalex.org/W2590882018","https://openalex.org/W2734865725","https://openalex.org/W3183315860"],"related_works":["https://openalex.org/W174356015","https://openalex.org/W2048805346","https://openalex.org/W61060296","https://openalex.org/W3035164848","https://openalex.org/W1816014094","https://openalex.org/W2305531760","https://openalex.org/W2258010065","https://openalex.org/W2772835986","https://openalex.org/W2015888813","https://openalex.org/W2055868857","https://openalex.org/W2148856424","https://openalex.org/W69133773","https://openalex.org/W2073464705","https://openalex.org/W2567811845","https://openalex.org/W3125157534","https://openalex.org/W315796958","https://openalex.org/W176087417","https://openalex.org/W62433044","https://openalex.org/W2100687784","https://openalex.org/W2096182168"],"abstract_inverted_index":{"Nonconvex":[0],"optimal":[1,100],"control":[2,47,101],"problems":[3,7,102],"governed":[4],"by":[5,41],"evolution":[6],"in":[8,50,64],"infinite-dimensional":[9],"spaces":[10],"(as,":[11],"e.g.,":[12],"parabolic":[13,99],"boundary-value":[14],"problems)":[15],"needs":[16],"a":[17,79],"continuous":[18],"(and":[19],"possibly":[20],"also":[21],"smooth)":[22],"extension":[23],"on":[24],"some":[25,51],"(preferably":[26],"convex)":[27],"compactification,":[28],"called":[29],"relaxation,":[30],"to":[31,38,98],"guarantee":[32],"existence":[33,106],"of":[34,53],"their":[35],"solutions":[36],"and":[37,107],"facilitate":[39],"analysis":[40],"relatively":[42],"conventional":[43],"tools.":[44],"When":[45],"the":[46,56],"is":[48,83,96],"valued":[49],"subsets":[52],"Lebesgue":[54],"spaces,":[55],"usual":[57],"extensions":[58],"are":[59],"either":[60],"too":[61,71],"coarse":[62],"(allowing":[63],"fact":[65],"only":[66],"very":[67],"restricted":[68],"nonlinearities)":[69],"or":[70],"fine":[72],"(being":[73],"nonmetrizable).":[74],"To":[75],"overcome":[76],"these":[77],"drawbacks,":[78],"compromising":[80],"convex":[81],"compactification":[82],"here":[84],"devised,":[85],"combining":[86],"classical":[87],"techniques":[88],"for":[89],"Young":[90],"measures":[91],"with":[92],"Choquet":[93],"theory.":[94],"This":[95],"applied":[97],"as":[103,105],"far":[104],"optimality":[108],"conditions":[109],"concerns.":[110]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2021-02-15T00:00:00"}