{"id":"https://openalex.org/W7164901729","doi":"https://doi.org/10.48550/arxiv.2606.17000","title":"The Complexity of Min-Max Optimization for Quadratic Polynomials","display_name":"The Complexity of Min-Max Optimization for Quadratic Polynomials","publication_year":2026,"publication_date":"2026-06-15","ids":{"openalex":"https://openalex.org/W7164901729","doi":"https://doi.org/10.48550/arxiv.2606.17000"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2606.17000","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2606.17000","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,"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":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2606.17000","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5068192992","display_name":"Martino Bernasconi","orcid":"https://orcid.org/0000-0002-8594-2528"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Bernasconi, Martino","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5138729573","display_name":"Matteo Castiglioni","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Castiglioni, Matteo","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5023478606","display_name":"Andrea Celli","orcid":"https://orcid.org/0000-0002-2046-4019"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Celli, Andrea","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5065826113","display_name":"Alexandros Hollender","orcid":"https://orcid.org/0000-0001-5255-9349"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Hollender, Alexandros","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"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/T11435","display_name":"Polynomial and algebraic computation","score":0.24789999425411224,"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/T11435","display_name":"Polynomial and algebraic computation","score":0.24789999425411224,"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":0.23999999463558197,"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/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.21220000088214874,"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/quadratic-equation","display_name":"Quadratic equation","score":0.5622000098228455},{"id":"https://openalex.org/keywords/hypercube","display_name":"Hypercube","score":0.5313000082969666},{"id":"https://openalex.org/keywords/inverse","display_name":"Inverse","score":0.5145000219345093},{"id":"https://openalex.org/keywords/variable","display_name":"Variable (mathematics)","score":0.49000000953674316},{"id":"https://openalex.org/keywords/quadratic-programming","display_name":"Quadratic programming","score":0.4011000096797943},{"id":"https://openalex.org/keywords/complex-quadratic-polynomial","display_name":"Complex quadratic polynomial","score":0.3847000002861023},{"id":"https://openalex.org/keywords/quadratic-unconstrained-binary-optimization","display_name":"Quadratic unconstrained binary optimization","score":0.3693999946117401},{"id":"https://openalex.org/keywords/difference-polynomials","display_name":"Difference polynomials","score":0.3610000014305115}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6990000009536743},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.5622000098228455},{"id":"https://openalex.org/C50820777","wikidata":"https://www.wikidata.org/wiki/Q213723","display_name":"Hypercube","level":2,"score":0.5313000082969666},{"id":"https://openalex.org/C207467116","wikidata":"https://www.wikidata.org/wiki/Q4385666","display_name":"Inverse","level":2,"score":0.5145000219345093},{"id":"https://openalex.org/C182365436","wikidata":"https://www.wikidata.org/wiki/Q50701","display_name":"Variable (mathematics)","level":2,"score":0.49000000953674316},{"id":"https://openalex.org/C81845259","wikidata":"https://www.wikidata.org/wiki/Q290117","display_name":"Quadratic programming","level":2,"score":0.4011000096797943},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.40049999952316284},{"id":"https://openalex.org/C6077466","wikidata":"https://www.wikidata.org/wiki/Q5156597","display_name":"Complex quadratic polynomial","level":3,"score":0.3847000002861023},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.37560001015663147},{"id":"https://openalex.org/C177179195","wikidata":"https://www.wikidata.org/wiki/Q7268372","display_name":"Quadratic unconstrained binary optimization","level":4,"score":0.3693999946117401},{"id":"https://openalex.org/C86607863","wikidata":"https://www.wikidata.org/wiki/Q5275279","display_name":"Difference polynomials","level":3,"score":0.3610000014305115},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.34689998626708984},{"id":"https://openalex.org/C179799912","wikidata":"https://www.wikidata.org/wiki/Q205084","display_name":"Computational complexity theory","level":2,"score":0.3165999948978424},{"id":"https://openalex.org/C21736991","wikidata":"https://www.wikidata.org/wiki/Q17006917","display_name":"Classical orthogonal polynomials","level":3,"score":0.3165000081062317},{"id":"https://openalex.org/C80695182","wikidata":"https://www.wikidata.org/wiki/Q864134","display_name":"Binary quadratic form","level":4,"score":0.30070000886917114},{"id":"https://openalex.org/C148764684","wikidata":"https://www.wikidata.org/wiki/Q621751","display_name":"Approximation algorithm","level":2,"score":0.2989000082015991},{"id":"https://openalex.org/C166437778","wikidata":"https://www.wikidata.org/wiki/Q50695","display_name":"Quadratic function","level":3,"score":0.2939000129699707},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.2930000126361847},{"id":"https://openalex.org/C135252773","wikidata":"https://www.wikidata.org/wiki/Q1567213","display_name":"Inverse problem","level":2,"score":0.28949999809265137},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.2856999933719635},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.28040000796318054},{"id":"https://openalex.org/C52537462","wikidata":"https://www.wikidata.org/wiki/Q5282055","display_name":"Discrete orthogonal polynomials","level":3,"score":0.26499998569488525},{"id":"https://openalex.org/C145242015","wikidata":"https://www.wikidata.org/wiki/Q774123","display_name":"Approximation theory","level":2,"score":0.26409998536109924},{"id":"https://openalex.org/C148043351","wikidata":"https://www.wikidata.org/wiki/Q4456944","display_name":"Current (fluid)","level":2,"score":0.25049999356269836}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2606.17000","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2606.17000","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,"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":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2606.17000","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2606.17000","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,"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":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"We":[0],"prove":[1],"that":[2],"computing":[3],"approximate":[4],"stationary":[5],"points":[6],"of":[7],"min-max":[8],"optimization":[9],"over":[10],"the":[11,22,35,47],"hypercube":[12],"is":[13,38],"PPAD-hard":[14],"for":[15,51],"quadratic":[16],"polynomials.":[17],"This":[18],"holds":[19],"even":[20],"when":[21],"polynomials":[23],"are":[24],"multilinear,":[25],"each":[26],"variable":[27],"appears":[28],"in":[29],"at":[30],"most":[31],"three":[32],"monomials,":[33],"and":[34],"approximation":[36],"factor":[37],"inverse":[39],"polynomial.":[40],"As":[41],"a":[42],"direct":[43],"consequence,":[44],"we":[45],"obtain":[46],"first":[48],"PPAD-hardness":[49],"results":[50],"two-team":[52],"zero-sum":[53],"polymatrix":[54],"games.":[55]},"counts_by_year":[],"updated_date":"2026-07-28T07:46:37.118299","created_date":"2026-06-17T00:00:00"}
