{"id":"https://openalex.org/W2605348669","doi":"https://doi.org/10.1007/s10957-018-1328-z","title":"Envelope Functions: Unifications and Further Properties","display_name":"Envelope Functions: Unifications and Further Properties","publication_year":2018,"publication_date":"2018-06-12","ids":{"openalex":"https://openalex.org/W2605348669","doi":"https://doi.org/10.1007/s10957-018-1328-z","mag":"2605348669"},"language":"en","primary_location":{"id":"doi:10.1007/s10957-018-1328-z","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10957-018-1328-z","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10957-018-1328-z.pdf","source":{"id":"https://openalex.org/S52430896","display_name":"Journal of Optimization Theory and Applications","issn_l":"0022-3239","issn":["0022-3239","1573-2878"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Optimization Theory and Applications","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s10957-018-1328-z.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5030031115","display_name":"Pontus Giselsson","orcid":"https://orcid.org/0000-0003-1602-1204"},"institutions":[{"id":"https://openalex.org/I187531555","display_name":"Lund University","ror":"https://ror.org/012a77v79","country_code":"SE","type":"education","lineage":["https://openalex.org/I187531555"]}],"countries":["SE"],"is_corresponding":true,"raw_author_name":"Pontus Giselsson","raw_affiliation_strings":["Department of Automatic Control, Lund University, Box 118, SE-221 00, Lund, Sweden"],"affiliations":[{"raw_affiliation_string":"Department of Automatic Control, Lund University, Box 118, SE-221 00, Lund, Sweden","institution_ids":["https://openalex.org/I187531555"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5051310171","display_name":"Mattias F\u00e4lt","orcid":null},"institutions":[{"id":"https://openalex.org/I187531555","display_name":"Lund University","ror":"https://ror.org/012a77v79","country_code":"SE","type":"education","lineage":["https://openalex.org/I187531555"]}],"countries":["SE"],"is_corresponding":false,"raw_author_name":"Mattias F\u00e4lt","raw_affiliation_strings":["Department of Automatic Control, Lund University, Box 118, SE-221 00, Lund, Sweden"],"affiliations":[{"raw_affiliation_string":"Department of Automatic Control, Lund University, Box 118, SE-221 00, Lund, Sweden","institution_ids":["https://openalex.org/I187531555"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5030031115"],"corresponding_institution_ids":["https://openalex.org/I187531555"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":{"value":2390,"currency":"EUR","value_usd":2990},"fwci":1.0134,"has_fulltext":true,"cited_by_count":8,"citation_normalized_percentile":{"value":0.7164231,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"178","issue":"3","first_page":"673","last_page":"698"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9994000196456909,"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":0.9994000196456909,"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":0.9991999864578247,"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/T10545","display_name":"Optimization and Variational Analysis","score":0.9991000294685364,"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/envelope","display_name":"Envelope (radar)","score":0.7413259148597717},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.717457115650177},{"id":"https://openalex.org/keywords/smoothness","display_name":"Smoothness","score":0.6755052208900452},{"id":"https://openalex.org/keywords/convexity","display_name":"Convexity","score":0.6736742258071899},{"id":"https://openalex.org/keywords/theory-of-computation","display_name":"Theory of computation","score":0.6067771911621094},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.4959157407283783},{"id":"https://openalex.org/keywords/optimization-problem","display_name":"Optimization problem","score":0.45281097292900085},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.4504757821559906},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4501577913761139},{"id":"https://openalex.org/keywords/minification","display_name":"Minification","score":0.4206077456474304},{"id":"https://openalex.org/keywords/convex-function","display_name":"Convex function","score":0.4188605546951294},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.332266628742218},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.3219132423400879},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.23218685388565063},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.21468228101730347},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.07621580362319946}],"concepts":[{"id":"https://openalex.org/C65155139","wikidata":"https://www.wikidata.org/wiki/Q5380912","display_name":"Envelope (radar)","level":3,"score":0.7413259148597717},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.717457115650177},{"id":"https://openalex.org/C102634674","wikidata":"https://www.wikidata.org/wiki/Q868473","display_name":"Smoothness","level":2,"score":0.6755052208900452},{"id":"https://openalex.org/C72134830","wikidata":"https://www.wikidata.org/wiki/Q5166524","display_name":"Convexity","level":2,"score":0.6736742258071899},{"id":"https://openalex.org/C24858836","wikidata":"https://www.wikidata.org/wiki/Q844718","display_name":"Theory of computation","level":2,"score":0.6067771911621094},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4959157407283783},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.45281097292900085},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.4504757821559906},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4501577913761139},{"id":"https://openalex.org/C147764199","wikidata":"https://www.wikidata.org/wiki/Q6865248","display_name":"Minification","level":2,"score":0.4206077456474304},{"id":"https://openalex.org/C145446738","wikidata":"https://www.wikidata.org/wiki/Q319913","display_name":"Convex function","level":3,"score":0.4188605546951294},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.332266628742218},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.3219132423400879},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.23218685388565063},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.21468228101730347},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.07621580362319946},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0},{"id":"https://openalex.org/C106159729","wikidata":"https://www.wikidata.org/wiki/Q2294553","display_name":"Financial economics","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/C554190296","wikidata":"https://www.wikidata.org/wiki/Q47528","display_name":"Radar","level":2,"score":0.0},{"id":"https://openalex.org/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1007/s10957-018-1328-z","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10957-018-1328-z","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10957-018-1328-z.pdf","source":{"id":"https://openalex.org/S52430896","display_name":"Journal of Optimization Theory and Applications","issn_l":"0022-3239","issn":["0022-3239","1573-2878"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Optimization Theory and Applications","raw_type":"journal-article"},{"id":"pmh:oai:RePEc:spr:joptap:v:178:y:2018:i:3:d:10.1007_s10957-018-1328-z","is_oa":false,"landing_page_url":"http://link.springer.com/10.1007/s10957-018-1328-z","pdf_url":null,"source":{"id":"https://openalex.org/S4306401271","display_name":"RePEc: Research Papers in Economics","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I77793887","host_organization_name":"Federal Reserve Bank of St. Louis","host_organization_lineage":["https://openalex.org/I77793887"],"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":"article"},{"id":"pmh:oai:lup.lub.lu.se:621a87ae-86a0-4620-b09d-982d7ccb858e","is_oa":false,"landing_page_url":"https://lup.lub.lu.se/record/621a87ae-86a0-4620-b09d-982d7ccb858e","pdf_url":null,"source":{"id":"https://openalex.org/S4306400536","display_name":"Lund University Publications (Lund University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I187531555","host_organization_name":"Lund University","host_organization_lineage":["https://openalex.org/I187531555"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"ISSN: 0022-3239","raw_type":"text"}],"best_oa_location":{"id":"doi:10.1007/s10957-018-1328-z","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10957-018-1328-z","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10957-018-1328-z.pdf","source":{"id":"https://openalex.org/S52430896","display_name":"Journal of Optimization Theory and Applications","issn_l":"0022-3239","issn":["0022-3239","1573-2878"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Optimization Theory and Applications","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320320940","display_name":"Stiftelsen f\u00f6r\u00a0Strategisk Forskning","ror":"https://ror.org/044wr7g58"},{"id":"https://openalex.org/F4320321806","display_name":"Lunds Universitet","ror":"https://ror.org/012a77v79"},{"id":"https://openalex.org/F4320322581","display_name":"Vetenskapsr\u00e5det","ror":"https://ror.org/03zttf063"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2605348669.pdf","grobid_xml":"https://content.openalex.org/works/W2605348669.grobid-xml"},"referenced_works_count":40,"referenced_works":["https://openalex.org/W205960364","https://openalex.org/W1525779601","https://openalex.org/W1551360398","https://openalex.org/W1953936588","https://openalex.org/W1981220107","https://openalex.org/W1985077192","https://openalex.org/W2003372231","https://openalex.org/W2004291775","https://openalex.org/W2019569173","https://openalex.org/W2037603831","https://openalex.org/W2045079045","https://openalex.org/W2056510226","https://openalex.org/W2074214991","https://openalex.org/W2085440994","https://openalex.org/W2092663520","https://openalex.org/W2094877794","https://openalex.org/W2164278908","https://openalex.org/W2173413132","https://openalex.org/W2235143186","https://openalex.org/W2244987555","https://openalex.org/W2310612435","https://openalex.org/W2321466613","https://openalex.org/W2329579984","https://openalex.org/W2466668725","https://openalex.org/W2579401700","https://openalex.org/W2607928667","https://openalex.org/W2755368735","https://openalex.org/W2951948474","https://openalex.org/W2962964459","https://openalex.org/W2963000588","https://openalex.org/W3029645440","https://openalex.org/W3099831354","https://openalex.org/W3101644375","https://openalex.org/W3141595720","https://openalex.org/W4229650096","https://openalex.org/W4249513058","https://openalex.org/W4249667877","https://openalex.org/W4285719527","https://openalex.org/W4292363360","https://openalex.org/W6601216650"],"related_works":["https://openalex.org/W2940405130","https://openalex.org/W2363211409","https://openalex.org/W2376481828","https://openalex.org/W2390990501","https://openalex.org/W2035309570","https://openalex.org/W2002792507","https://openalex.org/W2348787543","https://openalex.org/W4226280031","https://openalex.org/W4387602064","https://openalex.org/W2044122222"],"abstract_inverted_index":{"Forward\u2013backward":[0],"and":[1,23,39,42,82],"Douglas\u2013Rachford":[2,24],"splitting":[3],"are":[4],"methods":[5,112],"for":[6,18,57,99],"structured":[7],"nonsmooth":[8,19,60],"optimization.":[9],"With":[10],"the":[11,21,48,51,65,90,100,110],"aim":[12],"to":[13,118],"use":[14],"smooth":[15,67],"optimization":[16,61],"techniques":[17],"problems,":[20],"forward\u2013backward":[22],"envelopes":[25],"where":[26],"recently":[27],"proposed.":[28],"Under":[29],"specific":[30],"problem":[31],"assumptions,":[32],"these":[33],"envelope":[34,69,78,92,121],"functions":[35],"have":[36],"favorable":[37],"smoothness":[38],"convexity":[40],"properties":[41,88],"their":[43,119],"stationary":[44],"points":[45],"coincide":[46],"with":[47],"fixed-points":[49],"of":[50,89,109],"underlying":[52,111],"algorithm":[53],"operators.":[54],"This":[55],"allows":[56],"solving":[58],"such":[59],"problems":[62],"by":[63],"minimizing":[64],"corresponding":[66,96],"convex":[68],"function.":[70],"In":[71],"this":[72],"paper,":[73],"we":[74],"present":[75,105],"a":[76,106],"general":[77,91],"function":[79,93],"that":[80,94],"unifies":[81],"generalizes":[83],"existing":[84],"ones.":[85],"We":[86,103],"provide":[87],"sharpen":[95],"known":[97],"results":[98],"special":[101],"cases.":[102],"also":[104],"new":[107],"interpretation":[108],"as":[113],"being":[114],"majorization\u2013minimization":[115],"algorithms":[116],"applied":[117],"respective":[120],"functions.":[122]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":3}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
