{"id":"https://openalex.org/W2888358248","doi":"https://doi.org/10.1137/18m1209088","title":"Polar Convolution","display_name":"Polar Convolution","publication_year":2019,"publication_date":"2019-01-01","ids":{"openalex":"https://openalex.org/W2888358248","doi":"https://doi.org/10.1137/18m1209088","mag":"2888358248"},"language":"en","primary_location":{"id":"doi:10.1137/18m1209088","is_oa":false,"landing_page_url":"https://doi.org/10.1137/18m1209088","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":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5054518852","display_name":"Michael P. Friedlander","orcid":"https://orcid.org/0000-0003-0222-5222"},"institutions":[{"id":"https://openalex.org/I141945490","display_name":"University of British Columbia","ror":"https://ror.org/03rmrcq20","country_code":"CA","type":"education","lineage":["https://openalex.org/I141945490"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Michael P. Friedlander","raw_affiliation_strings":[", University of British Columbia"],"raw_orcid":"https://orcid.org/0000-0003-0222-5222","affiliations":[{"raw_affiliation_string":", University of British Columbia","institution_ids":["https://openalex.org/I141945490"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5021061998","display_name":"Ives Mac\u00eado","orcid":"https://orcid.org/0000-0002-7993-7298"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Ives Mac\u00eado","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5065214298","display_name":"Ting Kei Pong","orcid":"https://orcid.org/0000-0001-5862-2986"},"institutions":[{"id":"https://openalex.org/I14243506","display_name":"Hong Kong Polytechnic University","ror":"https://ror.org/0030zas98","country_code":"HK","type":"education","lineage":["https://openalex.org/I14243506"]}],"countries":["HK"],"is_corresponding":false,"raw_author_name":"Ting Kei Pong","raw_affiliation_strings":["[Hong Kong Polytechnic Univ.]"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"[Hong Kong Polytechnic Univ.]","institution_ids":["https://openalex.org/I14243506"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.9711,"has_fulltext":false,"cited_by_count":6,"citation_normalized_percentile":{"value":0.71619166,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"29","issue":"2","first_page":"1366","last_page":"1391"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":1.0,"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"}},"topics":[{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":1.0,"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/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9983999729156494,"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/T11205","display_name":"Numerical methods in inverse problems","score":0.982200026512146,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7902318835258484},{"id":"https://openalex.org/keywords/convolution","display_name":"Convolution (computer science)","score":0.555338442325592},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.39314836263656616},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3767015337944031},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.3349328935146332},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.145918607711792},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.1181587278842926}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7902318835258484},{"id":"https://openalex.org/C45347329","wikidata":"https://www.wikidata.org/wiki/Q5166604","display_name":"Convolution (computer science)","level":3,"score":0.555338442325592},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.39314836263656616},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3767015337944031},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3349328935146332},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.145918607711792},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.1181587278842926},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/18m1209088","is_oa":false,"landing_page_url":"https://doi.org/10.1137/18m1209088","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:ira.lib.polyu.edu.hk:10397/89215","is_oa":false,"landing_page_url":"http://hdl.handle.net/10397/89215","pdf_url":null,"source":{"id":"https://openalex.org/S4306400205","display_name":"PolyU Institutional Research Archive (Hong Kong Polytechnic University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I14243506","host_organization_name":"Hong Kong Polytechnic University","host_organization_lineage":["https://openalex.org/I14243506"],"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":"Journal/Magazine Article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G136863935","display_name":null,"funder_award_id":"N00014-17-1-2009","funder_id":"https://openalex.org/F4320337345","funder_display_name":"Office of Naval Research"},{"id":"https://openalex.org/G8898485466","display_name":null,"funder_award_id":"PolyU253008/15p","funder_id":"https://openalex.org/F4320321592","funder_display_name":"Research Grants Council, University Grants Committee"}],"funders":[{"id":"https://openalex.org/F4320321592","display_name":"Research Grants Council, University Grants Committee","ror":"https://ror.org/00djwmt25"},{"id":"https://openalex.org/F4320337345","display_name":"Office of Naval Research","ror":"https://ror.org/00rk2pe57"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":16,"referenced_works":["https://openalex.org/W205960364","https://openalex.org/W1499439642","https://openalex.org/W1503425191","https://openalex.org/W1972010412","https://openalex.org/W1999834501","https://openalex.org/W2078204800","https://openalex.org/W2108763700","https://openalex.org/W2114605231","https://openalex.org/W2119058682","https://openalex.org/W2167732364","https://openalex.org/W2484049713","https://openalex.org/W2528863944","https://openalex.org/W2543381247","https://openalex.org/W2963205865","https://openalex.org/W3100158133","https://openalex.org/W4254078441"],"related_works":["https://openalex.org/W2073495840","https://openalex.org/W2334093999","https://openalex.org/W3134991707","https://openalex.org/W2071794268","https://openalex.org/W2937560759","https://openalex.org/W2043057586","https://openalex.org/W2594599357","https://openalex.org/W1989920940","https://openalex.org/W4249580765","https://openalex.org/W2014478174"],"abstract_inverted_index":{"The":[0],"Moreau":[1,52],"envelope":[2,53,63,75],"is":[3,16,114],"one":[4],"of":[5,23,50,73,80,94,101,111],"the":[6,19,32,40,51,55,61,74,81,92],"key":[7],"convexity-preserving":[8],"functional":[9],"operations":[10],"in":[11,88,91],"convex":[12,27],"analysis,":[13],"and":[14,21,54,64,78,90],"it":[15],"central":[17],"to":[18,44,105],"development":[20],"analysis":[22],"many":[24],"approaches":[25],"for":[26,34,96,108],"optimization.":[28,98],"This":[29],"paper":[30],"develops":[31],"theory":[33],"an":[35],"analogous":[36],"convolution":[37],"operation,":[38],"called":[39],"polar":[41,62],"envelope,":[42],"specialized":[43],"gauge":[45,97],"functions.":[46],"Many":[47],"important":[48,86],"properties":[49,70],"proximal":[56,67,82],"map":[57],"are":[58],"mirrored":[59],"by":[60],"its":[65],"corresponding":[66],"map.":[68],"These":[69],"include":[71],"smoothness":[72],"function,":[76],"uniqueness,":[77],"continuity":[79],"map,":[83],"which":[84,104],"play":[85],"roles":[87],"duality":[89],"construction":[93],"algorithms":[95,107],"A":[99],"suite":[100],"tools":[102],"with":[103],"build":[106],"this":[109],"family":[110],"optimization":[112],"problems":[113],"thus":[115],"established.":[116]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2018-08-31T00:00:00"}