{"id":"https://openalex.org/W7123540935","doi":"https://doi.org/10.48550/arxiv.2601.07076","title":"Primal-Dual algorithms for Abstract convex functions with respect to quadratic functions","display_name":"Primal-Dual algorithms for Abstract convex functions with respect to quadratic functions","publication_year":2026,"publication_date":"2026-01-11","ids":{"openalex":"https://openalex.org/W7123540935","doi":"https://doi.org/10.48550/arxiv.2601.07076"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2601.07076","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2601.07076","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"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":"article"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2601.07076","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5030264329","display_name":"Ewa Bednarczuk","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Bednarczuk, Ewa","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5122925531","display_name":"The Hung Tran","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Tran, The Hung","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"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":0.9635000228881836,"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":0.9635000228881836,"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":0.0066999997943639755,"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/T12661","display_name":"Iterative Methods for Nonlinear Equations","score":0.004800000227987766,"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/quadratic-equation","display_name":"Quadratic equation","score":0.5454000234603882},{"id":"https://openalex.org/keywords/convex-function","display_name":"Convex function","score":0.5349000096321106},{"id":"https://openalex.org/keywords/convex-optimization","display_name":"Convex optimization","score":0.490200012922287},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.4887999892234802},{"id":"https://openalex.org/keywords/convex-analysis","display_name":"Convex analysis","score":0.44519999623298645},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.4431999921798706},{"id":"https://openalex.org/keywords/saddle-point","display_name":"Saddle point","score":0.43970000743865967},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.4368000030517578},{"id":"https://openalex.org/keywords/quadratic-programming","display_name":"Quadratic programming","score":0.41850000619888306}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7311999797821045},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.5454000234603882},{"id":"https://openalex.org/C145446738","wikidata":"https://www.wikidata.org/wiki/Q319913","display_name":"Convex function","level":3,"score":0.5349000096321106},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.490200012922287},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.4887999892234802},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.45320001244544983},{"id":"https://openalex.org/C12108790","wikidata":"https://www.wikidata.org/wiki/Q2234833","display_name":"Convex analysis","level":4,"score":0.44519999623298645},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.4431999921798706},{"id":"https://openalex.org/C2681867","wikidata":"https://www.wikidata.org/wiki/Q690935","display_name":"Saddle point","level":2,"score":0.43970000743865967},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.4368000030517578},{"id":"https://openalex.org/C81845259","wikidata":"https://www.wikidata.org/wiki/Q290117","display_name":"Quadratic programming","level":2,"score":0.41850000619888306},{"id":"https://openalex.org/C111110010","wikidata":"https://www.wikidata.org/wiki/Q2627315","display_name":"Convex combination","level":4,"score":0.40720000863075256},{"id":"https://openalex.org/C50862404","wikidata":"https://www.wikidata.org/wiki/Q3075259","display_name":"Proper convex function","level":5,"score":0.39259999990463257},{"id":"https://openalex.org/C166437778","wikidata":"https://www.wikidata.org/wiki/Q50695","display_name":"Quadratic function","level":3,"score":0.39149999618530273},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.37139999866485596},{"id":"https://openalex.org/C2777127463","wikidata":"https://www.wikidata.org/wiki/Q10862618","display_name":"Saddle","level":2,"score":0.3490000069141388},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.33809998631477356},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.33340001106262207},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.33320000767707825},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.32580000162124634},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.3190999925136566},{"id":"https://openalex.org/C122268817","wikidata":"https://www.wikidata.org/wiki/Q2020318","display_name":"Frank\u2013Wolfe algorithm","level":5,"score":0.3086000084877014},{"id":"https://openalex.org/C206194317","wikidata":"https://www.wikidata.org/wiki/Q1138624","display_name":"Convex hull","level":3,"score":0.29330000281333923},{"id":"https://openalex.org/C79187972","wikidata":"https://www.wikidata.org/wiki/Q2654791","display_name":"Conic optimization","level":5,"score":0.2874999940395355},{"id":"https://openalex.org/C49870271","wikidata":"https://www.wikidata.org/wiki/Q193657","display_name":"Convex set","level":4,"score":0.27720001339912415},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.2766999900341034},{"id":"https://openalex.org/C200661725","wikidata":"https://www.wikidata.org/wiki/Q289500","display_name":"Subderivative","level":4,"score":0.27570000290870667},{"id":"https://openalex.org/C58385900","wikidata":"https://www.wikidata.org/wiki/Q5347254","display_name":"Effective domain","level":5,"score":0.2630000114440918}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2601.07076","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2601.07076","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"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":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2601.07076","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2601.07076","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"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":"article"},"sustainable_development_goals":[{"display_name":"Reduced inequalities","score":0.4598841965198517,"id":"https://metadata.un.org/sdg/10"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"We":[0,21,38],"consider":[1],"the":[2,7,16,26,33],"saddle":[3],"point":[4],"problem":[5],"where":[6],"objective":[8],"functions":[9],"are":[10],"abstract":[11,28],"convex":[12],"with":[13],"respect":[14],"to":[15],"class":[17],"of":[18],"quadratic":[19],"functions.":[20],"propose":[22],"primal-dual":[23],"algorithms":[24,41],"using":[25],"corresponding":[27],"proximal":[29],"operator":[30],"and":[31],"investigate":[32],"convergence":[34],"under":[35],"certain":[36],"restrictions.":[37],"test":[39],"our":[40],"by":[42],"several":[43],"numerical":[44],"examples.":[45]},"counts_by_year":[],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2026-01-14T00:00:00"}