{"id":"https://openalex.org/W7204771883","doi":"https://doi.org/10.48550/arxiv.2608.28319","title":"First-order approximations of multifunctions defined implicitly by \"split\" feasibility problems with applications to optimization","display_name":"First-order approximations of multifunctions defined implicitly by \"split\" feasibility problems with applications to optimization","publication_year":2026,"publication_date":"2026-08-28","ids":{"openalex":"https://openalex.org/W7204771883","doi":"https://doi.org/10.48550/arxiv.2608.28319"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2608.28319","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.28319","pdf_url":"https://arxiv.org/pdf/2608.28319","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2608.28319","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5003747785","display_name":"Amos Uderzo","orcid":"https://orcid.org/0000-0001-8120-159X","observed_orcids":["https://orcid.org/0000-0001-8120-159X"]},"institutions":[{"id":"https://openalex.org/I66752286","display_name":"University of Milano-Bicocca","ror":"https://ror.org/01ynf4891","country_code":"IT","type":"education","lineage":["https://openalex.org/I66752286"]}],"countries":["IT"],"is_corresponding":true,"raw_author_name":"Uderzo, Amos","raw_affiliation_strings":["Department of Mathematics and Applications - Universit\u00e0 di Milano-Bicocca Deutsche Bank Building 1 - Milan , MI 20125 , Italy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Applications - Universit\u00e0 di Milano-Bicocca Deutsche Bank Building 1 - Milan , MI 20125 , Italy","institution_ids":["https://openalex.org/I66752286"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5003747785"],"corresponding_institution_ids":["https://openalex.org/I66752286"],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10545","display_name":"Optimization and Variational Analysis","score":1.0,"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"}},"topics":[{"id":"https://openalex.org/T10545","display_name":"Optimization and Variational Analysis","score":1.0,"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/T12809","display_name":"Contact Mechanics and Variational Inequalities","score":0.0,"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":0.0,"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/split-feasibility-problem","display_name":"split feasibility problem","score":0.7950000166893005},{"id":"https://openalex.org/keywords/set-valued-mappings","display_name":"set-valued mappings","score":0.7289999723434448},{"id":"https://openalex.org/keywords/solution-map","display_name":"solution map","score":0.8190000057220459},{"id":"https://openalex.org/keywords/outer-approximation","display_name":"outer approximation","score":0.6169999837875366},{"id":"https://openalex.org/keywords/inner-approximation","display_name":"inner approximation","score":0.9879999756813049},{"id":"https://openalex.org/keywords/convex-feasibility-problem","display_name":"convex feasibility problem","score":0.9120000004768372},{"id":"https://openalex.org/keywords/optimality-conditions","display_name":"optimality conditions","score":0.8960000276565552}],"concepts":[{"id":"https://openalex.org/C165464430","wikidata":"https://www.wikidata.org/wiki/Q1570441","display_name":"Parameterized complexity","level":2,"score":0.7555000185966492},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.690500020980835},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.5443999767303467},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5146999955177307},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.4837000072002411},{"id":"https://openalex.org/C12713177","wikidata":"https://www.wikidata.org/wiki/Q1900281","display_name":"Perspective (graphical)","level":2,"score":0.4287000000476837},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.427700012922287},{"id":"https://openalex.org/C193386753","wikidata":"https://www.wikidata.org/wiki/Q1130396","display_name":"Approximations of \u03c0","level":2,"score":0.4172999858856201},{"id":"https://openalex.org/C93226319","wikidata":"https://www.wikidata.org/wiki/Q193137","display_name":"Differential (mechanical device)","level":2,"score":0.38530001044273376},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.352400004863739},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.34869998693466187},{"id":"https://openalex.org/C111771559","wikidata":"https://www.wikidata.org/wiki/Q66295","display_name":"Derivative (finance)","level":2,"score":0.34290000796318054},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.325300008058548},{"id":"https://openalex.org/C112313634","wikidata":"https://www.wikidata.org/wiki/Q7886648","display_name":"Complement (music)","level":5,"score":0.28999999165534973},{"id":"https://openalex.org/C145446738","wikidata":"https://www.wikidata.org/wiki/Q319913","display_name":"Convex function","level":3,"score":0.28760001063346863},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2540000081062317}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2608.28319","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.28319","pdf_url":"https://arxiv.org/pdf/2608.28319","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2608.28319","doi":"https://doi.org/10.48550/arxiv.2608.28319","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2608.28319","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2608.28319","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.28319","pdf_url":"https://arxiv.org/pdf/2608.28319","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7204771883.pdf","grobid_xml":"https://content.openalex.org/works/W7204771883.grobid-xml"},"referenced_works_count":1,"referenced_works":["https://openalex.org/W7147080310"],"related_works":["https://openalex.org/W7147080310","https://openalex.org/W2075308281","https://openalex.org/W1973963981","https://openalex.org/W1989629680","https://openalex.org/W4415773637","https://openalex.org/W1995063608","https://openalex.org/W1974856389","https://openalex.org/W3188980910","https://openalex.org/W1974189852","https://openalex.org/W2038106124"],"abstract_inverted_index":{"In":[0],"the":[1,65,70,83,101],"present":[2],"paper,":[3],"a":[4,19,24,34,58,89],"study":[5],"is":[6,91],"made":[7],"of":[8,12,26,36,52,64,69,80,82,97,103],"first-order":[9],"differential":[10],"properties":[11],"certain":[13],"multifunctions,":[14],"which":[15,75],"are":[16,33,73,76],"defined":[17],"as":[18],"solution":[20,71],"map":[21,72],"associated":[22],"with":[23,109],"family":[25],"parameterized":[27],"``split\"":[28,110],"feasibility":[29,38,111],"problems.":[30],"The":[31],"latter":[32],"class":[35],"convex":[37],"problems,":[39],"whose":[40],"specific":[41],"structure":[42],"makes":[43],"them":[44],"suitable":[45],"for":[46,94,106],"well-established":[47],"applications":[48],"in":[49,78,100],"several":[50],"areas":[51],"engineering":[53],"and":[54,61],"systems":[55],"biology.":[56],"As":[57,86],"result,":[59],"inner":[60],"outer":[62],"approximations":[63],"graphical":[66],"(contingent)":[67],"derivative":[68],"provided,":[74],"expressed":[77],"terms":[79],"derivatives":[81],"problem":[84],"data.":[85],"an":[87],"application,":[88],"perspective":[90],"also":[92],"discussed":[93],"employing":[95],"some":[96],"these":[98],"achievements":[99],"formulation":[102],"optimality":[104],"conditions":[105],"mathematical":[107],"programs":[108],"constraints.":[112]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-09-01T00:00:00"}
