{"id":"https://openalex.org/W2031494345","doi":"https://doi.org/10.1007/bf00120662","title":"Quadratic programming with one negative eigenvalue is NP-hard","display_name":"Quadratic programming with one negative eigenvalue is NP-hard","publication_year":1991,"publication_date":"1991-01-01","ids":{"openalex":"https://openalex.org/W2031494345","doi":"https://doi.org/10.1007/bf00120662","mag":"2031494345"},"language":"en","primary_location":{"id":"doi:10.1007/bf00120662","is_oa":false,"landing_page_url":"https://doi.org/10.1007/bf00120662","pdf_url":null,"source":{"id":"https://openalex.org/S115925768","display_name":"Journal of Global Optimization","issn_l":"0925-5001","issn":["0925-5001","1573-2916"],"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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Global Optimization","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5063808461","display_name":"P\u00e3nos M. Pardalos","orcid":"https://orcid.org/0000-0003-2824-101X"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Panos M. Pardalos","raw_affiliation_strings":["Department of Computer Science, Pennsylvania State University, 16802, University Park, PA, U.S.A","Department of Computer Science, Pennsylvania State University, University Park, U.S.A"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science, Pennsylvania State University, 16802, University Park, PA, U.S.A","institution_ids":[]},{"raw_affiliation_string":"Department of Computer Science, Pennsylvania State University, University Park, U.S.A","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5018511273","display_name":"Stephen A. Vavasis","orcid":"https://orcid.org/0000-0003-1519-6264"},"institutions":[{"id":"https://openalex.org/I205783295","display_name":"Cornell University","ror":"https://ror.org/05bnh6r87","country_code":"US","type":"education","lineage":["https://openalex.org/I205783295"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Stephen A. Vavasis","raw_affiliation_strings":["Department of Computer Science, Cornell University, 14853, Ithaca, NY, U.S.A","Department of Computer Science, Cornell University, Ithaca, U.S.A"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science, Cornell University, 14853, Ithaca, NY, U.S.A","institution_ids":[]},{"raw_affiliation_string":"Department of Computer Science, Cornell University, Ithaca, U.S.A","institution_ids":["https://openalex.org/I205783295"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5063808461"],"corresponding_institution_ids":[],"apc_list":{"value":2190,"currency":"EUR","value_usd":2780},"apc_paid":null,"fwci":8.3609,"has_fulltext":false,"cited_by_count":508,"citation_normalized_percentile":{"value":0.97992192,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":99,"max":100},"biblio":{"volume":"1","issue":"1","first_page":"15","last_page":"22"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9987000226974487,"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"}},"topics":[{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9987000226974487,"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/T12072","display_name":"Machine Learning and Algorithms","score":0.9851999878883362,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/T10545","display_name":"Optimization and Variational Analysis","score":0.972000002861023,"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/mathematics","display_name":"Mathematics","score":0.8160712718963623},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.7959728240966797},{"id":"https://openalex.org/keywords/quadratic-programming","display_name":"Quadratic programming","score":0.7199559807777405},{"id":"https://openalex.org/keywords/quadratic-equation","display_name":"Quadratic equation","score":0.6646038293838501},{"id":"https://openalex.org/keywords/quadratic-function","display_name":"Quadratic function","score":0.6474902629852295},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.4810355305671692},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.454039990901947},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.42533040046691895},{"id":"https://openalex.org/keywords/quadratically-constrained-quadratic-program","display_name":"Quadratically constrained quadratic program","score":0.42012301087379456},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3568838834762573},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.29480886459350586},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.05691686272621155}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8160712718963623},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.7959728240966797},{"id":"https://openalex.org/C81845259","wikidata":"https://www.wikidata.org/wiki/Q290117","display_name":"Quadratic programming","level":2,"score":0.7199559807777405},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.6646038293838501},{"id":"https://openalex.org/C166437778","wikidata":"https://www.wikidata.org/wiki/Q50695","display_name":"Quadratic function","level":3,"score":0.6474902629852295},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4810355305671692},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.454039990901947},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.42533040046691895},{"id":"https://openalex.org/C65148998","wikidata":"https://www.wikidata.org/wiki/Q7268373","display_name":"Quadratically constrained quadratic program","level":3,"score":0.42012301087379456},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3568838834762573},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.29480886459350586},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.05691686272621155},{"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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/bf00120662","is_oa":false,"landing_page_url":"https://doi.org/10.1007/bf00120662","pdf_url":null,"source":{"id":"https://openalex.org/S115925768","display_name":"Journal of Global Optimization","issn_l":"0925-5001","issn":["0925-5001","1573-2916"],"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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Global Optimization","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":9,"referenced_works":["https://openalex.org/W1568612004","https://openalex.org/W1978344132","https://openalex.org/W1993200481","https://openalex.org/W1995246641","https://openalex.org/W2011039300","https://openalex.org/W2018556306","https://openalex.org/W2039526985","https://openalex.org/W2043339930","https://openalex.org/W2079135578"],"related_works":["https://openalex.org/W4293088966","https://openalex.org/W2364127131","https://openalex.org/W2917463375","https://openalex.org/W2366868484","https://openalex.org/W2377851227","https://openalex.org/W2155888019","https://openalex.org/W3206492465","https://openalex.org/W2020990755","https://openalex.org/W4206704743","https://openalex.org/W2155219672"],"abstract_inverted_index":null,"counts_by_year":[{"year":2026,"cited_by_count":6},{"year":2025,"cited_by_count":27},{"year":2024,"cited_by_count":22},{"year":2023,"cited_by_count":18},{"year":2022,"cited_by_count":31},{"year":2021,"cited_by_count":31},{"year":2020,"cited_by_count":30},{"year":2019,"cited_by_count":28},{"year":2018,"cited_by_count":28},{"year":2017,"cited_by_count":37},{"year":2016,"cited_by_count":26},{"year":2015,"cited_by_count":20},{"year":2014,"cited_by_count":25},{"year":2013,"cited_by_count":28},{"year":2012,"cited_by_count":20}],"updated_date":"2026-03-31T07:56:22.981413","created_date":"2025-10-10T00:00:00"}
