{"id":"https://openalex.org/W2055664002","doi":"https://doi.org/10.1137/050648584","title":"Peeling Off a Nonconvex Cover of an Actual Convex Problem: Hidden Convexity","display_name":"Peeling Off a Nonconvex Cover of an Actual Convex Problem: Hidden Convexity","publication_year":2007,"publication_date":"2007-01-01","ids":{"openalex":"https://openalex.org/W2055664002","doi":"https://doi.org/10.1137/050648584","mag":"2055664002"},"language":"en","primary_location":{"id":"doi:10.1137/050648584","is_oa":false,"landing_page_url":"https://doi.org/10.1137/050648584","pdf_url":null,"source":{"id":"https://openalex.org/S928796702","display_name":"SIAM Journal on Optimization","issn_l":"1052-6234","issn":["1052-6234","1095-7189"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on 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/A5101619630","display_name":"Zhiyou Wu","orcid":"https://orcid.org/0000-0001-9107-5523"},"institutions":[{"id":"https://openalex.org/I126924076","display_name":"Chongqing Normal University","ror":"https://ror.org/01dcw5w74","country_code":"CN","type":"education","lineage":["https://openalex.org/I126924076"]},{"id":"https://openalex.org/I149672521","display_name":"Federation University","ror":"https://ror.org/05qbzwv83","country_code":"AU","type":"education","lineage":["https://openalex.org/I149672521"]}],"countries":["AU","CN"],"is_corresponding":true,"raw_author_name":"Z. Y. Wu","raw_affiliation_strings":["Chongqing Normal University","University of Ballarat"],"affiliations":[{"raw_affiliation_string":"Chongqing Normal University","institution_ids":["https://openalex.org/I126924076"]},{"raw_affiliation_string":"University of Ballarat","institution_ids":["https://openalex.org/I149672521"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100745907","display_name":"Duan Li","orcid":"https://orcid.org/0000-0001-9786-6238"},"institutions":[{"id":"https://openalex.org/I177725633","display_name":"Chinese University of Hong Kong","ror":"https://ror.org/00t33hh48","country_code":"CN","type":"education","lineage":["https://openalex.org/I177725633"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"D. Li","raw_affiliation_strings":["Chinese University of Hong Kong"],"affiliations":[{"raw_affiliation_string":"Chinese University of Hong Kong","institution_ids":["https://openalex.org/I177725633"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5020048395","display_name":"L. S. Zhang","orcid":null},"institutions":[{"id":"https://openalex.org/I113940042","display_name":"Shanghai University","ror":"https://ror.org/006teas31","country_code":"CN","type":"education","lineage":["https://openalex.org/I113940042"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"L. S. Zhang","raw_affiliation_strings":["Shanghai University"],"affiliations":[{"raw_affiliation_string":"Shanghai University","institution_ids":["https://openalex.org/I113940042"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5101830931","display_name":"Xiaohu Yang","orcid":"https://orcid.org/0000-0001-7427-9751"},"institutions":[{"id":"https://openalex.org/I126924076","display_name":"Chongqing Normal University","ror":"https://ror.org/01dcw5w74","country_code":"CN","type":"education","lineage":["https://openalex.org/I126924076"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"X. M. Yang","raw_affiliation_strings":["/Chongqing Normal University"],"affiliations":[{"raw_affiliation_string":"/Chongqing Normal University","institution_ids":["https://openalex.org/I126924076"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5101619630"],"corresponding_institution_ids":["https://openalex.org/I126924076","https://openalex.org/I149672521"],"apc_list":null,"apc_paid":null,"fwci":1.0006,"has_fulltext":false,"cited_by_count":16,"citation_normalized_percentile":{"value":0.76269157,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"18","issue":"2","first_page":"507","last_page":"536"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9998000264167786,"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":0.9998000264167786,"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/T10545","display_name":"Optimization and Variational Analysis","score":0.9911999702453613,"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/T10100","display_name":"Metaheuristic Optimization Algorithms Research","score":0.9864000082015991,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/convexity","display_name":"Convexity","score":0.9015871286392212},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7621541619300842},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.6361200213432312},{"id":"https://openalex.org/keywords/convex-optimization","display_name":"Convex optimization","score":0.5775663256645203},{"id":"https://openalex.org/keywords/cover","display_name":"Cover (algebra)","score":0.5764292478561401},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.5369399189949036},{"id":"https://openalex.org/keywords/verifiable-secret-sharing","display_name":"Verifiable secret sharing","score":0.4686051607131958},{"id":"https://openalex.org/keywords/quadratic-programming","display_name":"Quadratic programming","score":0.45283812284469604},{"id":"https://openalex.org/keywords/optimization-problem","display_name":"Optimization problem","score":0.43382614850997925},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.19347304105758667},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.18504035472869873}],"concepts":[{"id":"https://openalex.org/C72134830","wikidata":"https://www.wikidata.org/wiki/Q5166524","display_name":"Convexity","level":2,"score":0.9015871286392212},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7621541619300842},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.6361200213432312},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.5775663256645203},{"id":"https://openalex.org/C2780428219","wikidata":"https://www.wikidata.org/wiki/Q16952335","display_name":"Cover (algebra)","level":2,"score":0.5764292478561401},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.5369399189949036},{"id":"https://openalex.org/C85847156","wikidata":"https://www.wikidata.org/wiki/Q59015987","display_name":"Verifiable secret sharing","level":3,"score":0.4686051607131958},{"id":"https://openalex.org/C81845259","wikidata":"https://www.wikidata.org/wiki/Q290117","display_name":"Quadratic programming","level":2,"score":0.45283812284469604},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.43382614850997925},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.19347304105758667},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.18504035472869873},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C78519656","wikidata":"https://www.wikidata.org/wiki/Q101333","display_name":"Mechanical engineering","level":1,"score":0.0},{"id":"https://openalex.org/C106159729","wikidata":"https://www.wikidata.org/wiki/Q2294553","display_name":"Financial economics","level":1,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/050648584","is_oa":false,"landing_page_url":"https://doi.org/10.1137/050648584","pdf_url":null,"source":{"id":"https://openalex.org/S928796702","display_name":"SIAM Journal on Optimization","issn_l":"1052-6234","issn":["1052-6234","1095-7189"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Optimization","raw_type":"journal-article"},{"id":"pmh:vital:955","is_oa":false,"landing_page_url":"http://researchonline.federation.edu.au/vital/access/HandleResolver/1959.17/62438","pdf_url":null,"source":{"id":"https://openalex.org/S4306400234","display_name":"FedUni ResearchOnline (Federation University Australia)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210158496","host_organization_name":"Australian Federation of University Women \u2013 South Australia","host_organization_lineage":["https://openalex.org/I4210158496"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":15,"referenced_works":["https://openalex.org/W123093799","https://openalex.org/W1590012787","https://openalex.org/W1887931008","https://openalex.org/W1966056474","https://openalex.org/W1995866744","https://openalex.org/W2037764240","https://openalex.org/W2052044464","https://openalex.org/W2093404847","https://openalex.org/W2112289054","https://openalex.org/W2130311871","https://openalex.org/W2144180603","https://openalex.org/W2144997132","https://openalex.org/W2296319761","https://openalex.org/W2787523326","https://openalex.org/W2799135259"],"related_works":["https://openalex.org/W3159863825","https://openalex.org/W4314947455","https://openalex.org/W3003165794","https://openalex.org/W2003848856","https://openalex.org/W4287899549","https://openalex.org/W2151484740","https://openalex.org/W3199689622","https://openalex.org/W4375869934","https://openalex.org/W4225392794","https://openalex.org/W2246376079"],"abstract_inverted_index":{"Convexity":[0],"is,":[1],"without":[2],"a":[3,68,77],"doubt,":[4],"one":[5],"of":[6,67],"the":[7,34],"most":[8],"desirable":[9],"features":[10],"in":[11,19],"optimization.":[12],"Many":[13],"optimization":[14,62],"problems":[15],"that":[16],"are":[17,57],"nonconvex":[18],"their":[20],"original":[21],"settings":[22],"may":[23],"become":[24],"convex":[25,70],"after":[26],"performing":[27],"certain":[28],"equivalent":[29],"transformations.":[30],"This":[31],"paper":[32],"studies":[33],"conditions":[35,45,56],"for":[36,49,60],"such":[37],"hidden":[38,51,69],"convexity.":[39,52],"More":[40],"specifically,":[41],"some":[42],"transformation-independent":[43],"sufficient":[44,55],"have":[46],"been":[47],"derived":[48,54],"identifying":[50],"The":[53,64],"readily":[58],"verifiable":[59],"quadratic":[61],"problems.":[63],"global":[65],"minimizer":[66],"programming":[71],"problem":[72],"can":[73],"be":[74],"identified":[75],"using":[76],"local":[78],"search":[79],"algorithm.":[80]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":2},{"year":2015,"cited_by_count":1},{"year":2012,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}