{"id":"https://openalex.org/W4402279845","doi":"https://doi.org/10.1137/23m1575391","title":"Interpolation Conditions for Linear Operators and Applications to Performance Estimation Problems","display_name":"Interpolation Conditions for Linear Operators and Applications to Performance Estimation Problems","publication_year":2024,"publication_date":"2024-09-05","ids":{"openalex":"https://openalex.org/W4402279845","doi":"https://doi.org/10.1137/23m1575391"},"language":"en","primary_location":{"id":"doi:10.1137/23m1575391","is_oa":false,"landing_page_url":"https://doi.org/10.1137/23m1575391","pdf_url":null,"source":{"id":"https://openalex.org/S928796702","display_name":"SIAM Journal on Optimization","issn_l":"1052-6234","issn":["1052-6234","1095-7189"],"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 Optimization","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"http://hdl.handle.net/2078.1/293045","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5088640711","display_name":"Nizar Bousselmi","orcid":null},"institutions":[{"id":"https://openalex.org/I95674353","display_name":"UCLouvain","ror":"https://ror.org/02495e989","country_code":"BE","type":"education","lineage":["https://openalex.org/I95674353"]}],"countries":["BE"],"is_corresponding":false,"raw_author_name":"Nizar Bousselmi","raw_affiliation_strings":["UCLouvain, ICTEAM, Louvain-la-Neuve, Belgium"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"UCLouvain, ICTEAM, Louvain-la-Neuve, Belgium","institution_ids":["https://openalex.org/I95674353"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5003883360","display_name":"Julien M. Hendrickx","orcid":"https://orcid.org/0000-0001-8214-8292"},"institutions":[{"id":"https://openalex.org/I95674353","display_name":"UCLouvain","ror":"https://ror.org/02495e989","country_code":"BE","type":"education","lineage":["https://openalex.org/I95674353"]}],"countries":["BE"],"is_corresponding":false,"raw_author_name":"Julien M. Hendrickx","raw_affiliation_strings":["UCLouvain, ICTEAM, Louvain-la-Neuve, Belgium"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"UCLouvain, ICTEAM, Louvain-la-Neuve, Belgium","institution_ids":["https://openalex.org/I95674353"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5038754080","display_name":"Fran\u00e7ois Glineur","orcid":"https://orcid.org/0000-0002-5890-1093"},"institutions":[{"id":"https://openalex.org/I95674353","display_name":"UCLouvain","ror":"https://ror.org/02495e989","country_code":"BE","type":"education","lineage":["https://openalex.org/I95674353"]}],"countries":["BE"],"is_corresponding":false,"raw_author_name":"Fran\u00e7ois Glineur","raw_affiliation_strings":["UCLouvain, ICTEAM, Louvain-la-Neuve, Belgium, and UCLouvain, CORE, Louvain-la-Neuve, Belgium"],"raw_orcid":"https://orcid.org/0000-0002-5890-1093","affiliations":[{"raw_affiliation_string":"UCLouvain, ICTEAM, Louvain-la-Neuve, Belgium, and UCLouvain, CORE, Louvain-la-Neuve, Belgium","institution_ids":["https://openalex.org/I95674353"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.425,"has_fulltext":false,"cited_by_count":7,"citation_normalized_percentile":{"value":0.88165947,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"34","issue":"3","first_page":"3033","last_page":"3063"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11205","display_name":"Numerical methods in inverse problems","score":0.9993000030517578,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/T11205","display_name":"Numerical methods in inverse problems","score":0.9993000030517578,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/T11236","display_name":"Control Systems and Identification","score":0.9973000288009644,"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/T10792","display_name":"Matrix Theory and Algorithms","score":0.9972000122070312,"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/mathematics","display_name":"Mathematics","score":0.8353368043899536},{"id":"https://openalex.org/keywords/interpolation","display_name":"Interpolation (computer graphics)","score":0.6674641966819763},{"id":"https://openalex.org/keywords/linear-operators","display_name":"Linear operators","score":0.5613998770713806},{"id":"https://openalex.org/keywords/linear-interpolation","display_name":"Linear interpolation","score":0.5407130718231201},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.534092128276825},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5040382742881775},{"id":"https://openalex.org/keywords/bilinear-interpolation","display_name":"Bilinear interpolation","score":0.4657365381717682},{"id":"https://openalex.org/keywords/estimation","display_name":"Estimation","score":0.4249516427516937},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.23052281141281128},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.1658952236175537},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.15185651183128357},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.11670517921447754},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.09415274858474731},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.09143474698066711}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8353368043899536},{"id":"https://openalex.org/C137800194","wikidata":"https://www.wikidata.org/wiki/Q11713455","display_name":"Interpolation (computer graphics)","level":3,"score":0.6674641966819763},{"id":"https://openalex.org/C3019018024","wikidata":"https://www.wikidata.org/wiki/Q207643","display_name":"Linear operators","level":3,"score":0.5613998770713806},{"id":"https://openalex.org/C171836373","wikidata":"https://www.wikidata.org/wiki/Q2266329","display_name":"Linear interpolation","level":3,"score":0.5407130718231201},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.534092128276825},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5040382742881775},{"id":"https://openalex.org/C205203396","wikidata":"https://www.wikidata.org/wiki/Q612143","display_name":"Bilinear interpolation","level":2,"score":0.4657365381717682},{"id":"https://openalex.org/C96250715","wikidata":"https://www.wikidata.org/wiki/Q965330","display_name":"Estimation","level":2,"score":0.4249516427516937},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.23052281141281128},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.1658952236175537},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.15185651183128357},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.11670517921447754},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.09415274858474731},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.09143474698066711},{"id":"https://openalex.org/C187736073","wikidata":"https://www.wikidata.org/wiki/Q2920921","display_name":"Management","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C104114177","wikidata":"https://www.wikidata.org/wiki/Q79782","display_name":"Motion (physics)","level":2,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/23m1575391","is_oa":false,"landing_page_url":"https://doi.org/10.1137/23m1575391","pdf_url":null,"source":{"id":"https://openalex.org/S928796702","display_name":"SIAM Journal on Optimization","issn_l":"1052-6234","issn":["1052-6234","1095-7189"],"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 Optimization","raw_type":"journal-article"},{"id":"pmh:oai:dial.uclouvain.be:boreal:293045","is_oa":true,"landing_page_url":"http://hdl.handle.net/2078.1/293045","pdf_url":null,"source":{"id":"https://openalex.org/S4306401902","display_name":"Digital Access to Libraries (Universit\u00e9 catholique de Louvain (UCL), l'Universit\u00e9 de Namur (UNamur) and the Universit\u00e9 Saint-Louis (USL-B))","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I95674353","host_organization_name":"UCLouvain","host_organization_lineage":["https://openalex.org/I95674353"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"SIAM Journal on Optimization, Vol. 34, no.3, p. 3033-3063 (2024)","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"pmh:oai:dial.uclouvain.be:boreal:293045","is_oa":true,"landing_page_url":"http://hdl.handle.net/2078.1/293045","pdf_url":null,"source":{"id":"https://openalex.org/S4306401902","display_name":"Digital Access to Libraries (Universit\u00e9 catholique de Louvain (UCL), l'Universit\u00e9 de Namur (UNamur) and the Universit\u00e9 Saint-Louis (USL-B))","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I95674353","host_organization_name":"UCLouvain","host_organization_lineage":["https://openalex.org/I95674353"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"SIAM Journal on Optimization, Vol. 34, no.3, p. 3033-3063 (2024)","raw_type":"info:eu-repo/semantics/article"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320321584","display_name":"F\u00e9d\u00e9ration Wallonie-Bruxelles","ror":"https://ror.org/04q01pf08"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":50,"referenced_works":["https://openalex.org/W1547678669","https://openalex.org/W1931370844","https://openalex.org/W1962121538","https://openalex.org/W1979896658","https://openalex.org/W1998991750","https://openalex.org/W2019198051","https://openalex.org/W2045079045","https://openalex.org/W2046696187","https://openalex.org/W2054560172","https://openalex.org/W2071236014","https://openalex.org/W2092663520","https://openalex.org/W2100556411","https://openalex.org/W2103559027","https://openalex.org/W2114423093","https://openalex.org/W2220137601","https://openalex.org/W2241435520","https://openalex.org/W2273484141","https://openalex.org/W2473376220","https://openalex.org/W2498631646","https://openalex.org/W2508323711","https://openalex.org/W2512211375","https://openalex.org/W2615571142","https://openalex.org/W2791312514","https://openalex.org/W2953231121","https://openalex.org/W2963496223","https://openalex.org/W2963830980","https://openalex.org/W2989762492","https://openalex.org/W3037153379","https://openalex.org/W3041776387","https://openalex.org/W3043533097","https://openalex.org/W3048571829","https://openalex.org/W3095979953","https://openalex.org/W3098494876","https://openalex.org/W3100902858","https://openalex.org/W3102299214","https://openalex.org/W3104372163","https://openalex.org/W3136976430","https://openalex.org/W3158960540","https://openalex.org/W3203963792","https://openalex.org/W3217620259","https://openalex.org/W4205547947","https://openalex.org/W4229706427","https://openalex.org/W4250589301","https://openalex.org/W4281562381","https://openalex.org/W4283775266","https://openalex.org/W4296398255","https://openalex.org/W4321769656","https://openalex.org/W4323022350","https://openalex.org/W4375860094","https://openalex.org/W4379652848"],"related_works":["https://openalex.org/W2367652182","https://openalex.org/W2037074416","https://openalex.org/W1519931592","https://openalex.org/W2101207231","https://openalex.org/W2741873457","https://openalex.org/W2319983895","https://openalex.org/W2382426030","https://openalex.org/W2291214609","https://openalex.org/W3183609115","https://openalex.org/W2142192217"],"abstract_inverted_index":{"The":[0],"performance":[1,12],"estimation":[2],"problem":[3],"methodology":[4],"makes":[5],"it":[6,132],"possible":[7],"to":[8,103,122,135,148,160],"determine":[9],"theexact":[10],"worst-case":[11],"of":[13,45,64,89,117,164,168,193],"an":[14,32],"optimization":[15],"method.":[16],"In":[17,172],"this":[18,22,177,206],"work,":[19],"we":[20,111,174],"generalize":[21],"frameworkto":[23],"first-order":[24],"methods":[25],"involving":[26],"linear":[27,39,46,65,99],"operators.":[28,40],"This":[29],"extension":[30],"requires":[31],"explicit":[33],"formulationof":[34],"interpolation":[35,76],"conditions":[36,77,84],"for":[37,78,105,189],"those":[38],"We":[41,74,141],"consider":[42],"the":[43,62,96,114,118,123,144,157,165,169,190,194],"class":[44,63],"operators\\scrM":[47],":":[48],"x":[49],"\\mapsto":[50],"\\rightarrow":[51],"M":[52,56],"x,":[53],"where":[54],"matrix":[55],"has":[57,71],"bounded":[58,72],"singular":[59],"values,":[60],"and":[61,70,82,130,155,183],"operators,":[66],"whereM":[67],"is":[68,203],"symmetric":[69],"eigenvalues.":[73],"describe":[75],"these":[79,109],"classes,i.e.,":[80],"necessary":[81],"sufficient":[83],"that,":[85],"given":[86],"a":[87,98,138,162,185],"list":[88],"pairs":[90],"\\{":[91],"(xi,":[92],"yi)\\}":[93],",":[94,129,154],"characterize":[95],"existenceof":[97],"operator":[100],"mapping":[101],"xi":[102],"yi":[104],"all":[106],"i.":[107],"Using":[108],"conditions,":[110],"first":[112],"identify":[113],"exactworst-case":[115],"behavior":[116],"gradient":[119],"method":[120,146,178],"applied":[121,147],"composed":[124],"objective":[125],"h":[126],"\\circ":[127,152],"\\scrM":[128,136,153],"observethat":[131],"always":[133],"corresponds":[134],"being":[137],"scaling":[139],"operator.":[140],"then":[142],"investigate":[143],"Chambolle--Pock":[145],"f":[149],"+":[150],"g":[151],"improve":[156],"existing":[158],"analysis":[159],"obtain":[161,184],"proof":[163],"exactconvergence":[166],"rate":[167,188],"primal-dual":[170],"gap.":[171],"addition,":[173],"study":[175],"how":[176],"behaves":[179],"on":[180],"Lipschitzconvex":[181],"functions,":[182],"numerical":[186],"convergence":[187],"primal":[191],"accuracy":[192],"last":[195],"iterate.We":[196],"also":[197],"show":[198],"numerically":[199],"that":[200],"averaging":[201],"iterates":[202],"beneficial":[204],"in":[205],"setting.":[207]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":4}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
