{"id":"https://openalex.org/W7130374362","doi":"https://doi.org/10.1007/s10957-025-02911-1","title":"The Improvement Function Reformulation for Graphs of Minimal Point Mappings","display_name":"The Improvement Function Reformulation for Graphs of Minimal Point Mappings","publication_year":2026,"publication_date":"2026-02-18","ids":{"openalex":"https://openalex.org/W7130374362","doi":"https://doi.org/10.1007/s10957-025-02911-1"},"language":"en","primary_location":{"id":"doi:10.1007/s10957-025-02911-1","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10957-025-02911-1","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10957-025-02911-1.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/s10957-025-02911-1.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5009909310","display_name":"Stefan Schwarze","orcid":"https://orcid.org/0000-0002-1950-7114"},"institutions":[{"id":"https://openalex.org/I102335020","display_name":"Karlsruhe Institute of Technology","ror":"https://ror.org/04t3en479","country_code":"DE","type":"education","lineage":["https://openalex.org/I102335020","https://openalex.org/I1305996414"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Stefan Schwarze","raw_affiliation_strings":["Institute for Operations Research (IOR), Karlsruhe Institute of Technology (KIT), Karlsruhe, Germany"],"raw_orcid":"https://orcid.org/0000-0002-1950-7114","affiliations":[{"raw_affiliation_string":"Institute for Operations Research (IOR), Karlsruhe Institute of Technology (KIT), Karlsruhe, Germany","institution_ids":["https://openalex.org/I102335020"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5052388878","display_name":"Oliver Stein","orcid":"https://orcid.org/0000-0001-9514-6317"},"institutions":[{"id":"https://openalex.org/I102335020","display_name":"Karlsruhe Institute of Technology","ror":"https://ror.org/04t3en479","country_code":"DE","type":"education","lineage":["https://openalex.org/I102335020","https://openalex.org/I1305996414"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Oliver Stein","raw_affiliation_strings":["Institute for Operations Research (IOR), Karlsruhe Institute of Technology (KIT), Karlsruhe, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute for Operations Research (IOR), Karlsruhe Institute of Technology (KIT), Karlsruhe, Germany","institution_ids":["https://openalex.org/I102335020"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5009909310"],"corresponding_institution_ids":["https://openalex.org/I102335020"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":{"value":2390,"currency":"EUR","value_usd":2990},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.38463791,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"208","issue":"3","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":0.9843000173568726,"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":0.9843000173568726,"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/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.005100000184029341,"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/T11413","display_name":"Risk and Portfolio Optimization","score":0.0010999999940395355,"subfield":{"id":"https://openalex.org/subfields/1803","display_name":"Management Science and Operations Research"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/theory-of-computation","display_name":"Theory of computation","score":0.6351000070571899},{"id":"https://openalex.org/keywords/parametric-statistics","display_name":"Parametric statistics","score":0.6065000295639038},{"id":"https://openalex.org/keywords/intersection","display_name":"Intersection (aeronautics)","score":0.5938000082969666},{"id":"https://openalex.org/keywords/bilevel-optimization","display_name":"Bilevel optimization","score":0.5697000026702881},{"id":"https://openalex.org/keywords/nash-equilibrium","display_name":"Nash equilibrium","score":0.48919999599456787},{"id":"https://openalex.org/keywords/optimization-problem","display_name":"Optimization problem","score":0.4844000041484833},{"id":"https://openalex.org/keywords/point","display_name":"Point (geometry)","score":0.45239999890327454}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7695000171661377},{"id":"https://openalex.org/C24858836","wikidata":"https://www.wikidata.org/wiki/Q844718","display_name":"Theory of computation","level":2,"score":0.6351000070571899},{"id":"https://openalex.org/C117251300","wikidata":"https://www.wikidata.org/wiki/Q1849855","display_name":"Parametric statistics","level":2,"score":0.6065000295639038},{"id":"https://openalex.org/C64543145","wikidata":"https://www.wikidata.org/wiki/Q162942","display_name":"Intersection (aeronautics)","level":2,"score":0.5938000082969666},{"id":"https://openalex.org/C3309286","wikidata":"https://www.wikidata.org/wiki/Q4907693","display_name":"Bilevel optimization","level":3,"score":0.5697000026702881},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5242000222206116},{"id":"https://openalex.org/C46814582","wikidata":"https://www.wikidata.org/wiki/Q23389","display_name":"Nash equilibrium","level":2,"score":0.48919999599456787},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.4844000041484833},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.45239999890327454},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.429500013589859},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.38440001010894775},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.37139999866485596},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3508000075817108},{"id":"https://openalex.org/C146380142","wikidata":"https://www.wikidata.org/wiki/Q1137726","display_name":"Directed graph","level":2,"score":0.33980000019073486},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3111000061035156},{"id":"https://openalex.org/C52692508","wikidata":"https://www.wikidata.org/wiki/Q1333872","display_name":"Combinatorial optimization","level":2,"score":0.2897000014781952},{"id":"https://openalex.org/C2776045410","wikidata":"https://www.wikidata.org/wiki/Q25111241","display_name":"Parametric programming","level":3,"score":0.28839999437332153},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.28049999475479126},{"id":"https://openalex.org/C55660270","wikidata":"https://www.wikidata.org/wiki/Q5164377","display_name":"Constrained optimization","level":2,"score":0.26179999113082886},{"id":"https://openalex.org/C98375054","wikidata":"https://www.wikidata.org/wiki/Q442709","display_name":"Enclosure","level":2,"score":0.25029999017715454}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/s10957-025-02911-1","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10957-025-02911-1","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10957-025-02911-1.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:doi:10.5445/ir/1000190953","is_oa":true,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4406922384","display_name":"Open MIND","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"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":"Journal Article"}],"best_oa_location":{"id":"doi:10.1007/s10957-025-02911-1","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10957-025-02911-1","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10957-025-02911-1.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":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7130374362.pdf","grobid_xml":"https://content.openalex.org/works/W7130374362.grobid-xml"},"referenced_works_count":9,"referenced_works":["https://openalex.org/W1588628884","https://openalex.org/W1997949764","https://openalex.org/W2164498579","https://openalex.org/W3183306861","https://openalex.org/W4214631981","https://openalex.org/W4234277722","https://openalex.org/W4234761190","https://openalex.org/W4249513058","https://openalex.org/W4403083436"],"related_works":[],"abstract_inverted_index":{"Abstract":[0],"Graphs":[1],"of":[2,6,14,17,22,29,44,55,80,89],"minimal":[3,41,67],"point":[4,42,68],"mappings":[5],"parametric":[7,46],"optimization":[8,19,24,47],"problems":[9,20,48,58],"appear":[10],"in":[11,105],"the":[12,27,53,66,78,90],"definition":[13],"feasible":[15],"sets":[16],"bilevel":[18],"and":[21,26],"semi-infinite":[23],"problems,":[25],"intersection":[28],"multiple":[30],"such":[31],"graphs":[32,43],"defines":[33],"(generalized)":[34],"Nash":[35,82],"equilibria.":[36],"This":[37,62,85],"paper":[38],"shows":[39],"how":[40],"nonconvex":[45],"can":[49],"be":[50],"enclosed":[51],"with":[52,59,65],"help":[54],"well":[56,86],"structured":[57,87],"additional":[60],"parameters.":[61],"enclosure":[63,91],"coincides":[64],"graph":[69],"under":[70],"mild":[71],"assumptions.":[72],"We":[73,100],"specify":[74],"our":[75],"results":[76,104],"to":[77,95],"setting":[79],"generalized":[81],"equilibrium":[83],"problems.":[84],"formulation":[88],"makes":[92],"it":[93],"accessible":[94],"approximations":[96],"by":[97],"branch-and-bound":[98],"methods.":[99],"provide":[101],"corresponding":[102],"numerical":[103],"a":[106],"separate":[107],"paper.":[108]},"counts_by_year":[],"updated_date":"2026-03-13T14:20:09.374765","created_date":"2026-02-19T00:00:00"}
