{"id":"https://openalex.org/W2112356323","doi":"https://doi.org/10.1137/100790835","title":"Error Bounds for Some Semidefinite Programming Approaches to Polynomial Minimization on the Hypercube","display_name":"Error Bounds for Some Semidefinite Programming Approaches to Polynomial Minimization on the Hypercube","publication_year":2010,"publication_date":"2010-01-01","ids":{"openalex":"https://openalex.org/W2112356323","doi":"https://doi.org/10.1137/100790835","mag":"2112356323"},"language":"en","primary_location":{"id":"doi:10.1137/100790835","is_oa":false,"landing_page_url":"https://doi.org/10.1137/100790835","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/A5019341464","display_name":"Etienne de Klerk","orcid":"https://orcid.org/0000-0003-3377-0063"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Etienne de Klerk","raw_affiliation_strings":["E.deKlerk@uvt.nl#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"E.deKlerk@uvt.nl#TAB#","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5047819350","display_name":"Monique Laurent","orcid":"https://orcid.org/0000-0001-8474-2121"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Monique Laurent","raw_affiliation_strings":["M.Laurent@cwi.nl#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"M.Laurent@cwi.nl#TAB#","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":4.7039,"has_fulltext":false,"cited_by_count":53,"citation_normalized_percentile":{"value":0.95252091,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"20","issue":"6","first_page":"3104","last_page":"3120"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9994999766349792,"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":0.9994999766349792,"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":0.9983000159263611,"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/T11522","display_name":"VLSI and FPGA Design Techniques","score":0.9907000064849854,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/hypercube","display_name":"Hypercube","score":0.839257538318634},{"id":"https://openalex.org/keywords/semidefinite-programming","display_name":"Semidefinite programming","score":0.7665145397186279},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7662174701690674},{"id":"https://openalex.org/keywords/constructive","display_name":"Constructive","score":0.6308352947235107},{"id":"https://openalex.org/keywords/mathematical-proof","display_name":"Mathematical proof","score":0.5029940009117126},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.48340168595314026},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.47940346598625183},{"id":"https://openalex.org/keywords/degree","display_name":"Degree (music)","score":0.4481401741504669},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4466455578804016},{"id":"https://openalex.org/keywords/semidefinite-embedding","display_name":"Semidefinite embedding","score":0.4309879541397095},{"id":"https://openalex.org/keywords/minification","display_name":"Minification","score":0.429604172706604},{"id":"https://openalex.org/keywords/hierarchy","display_name":"Hierarchy","score":0.42577847838401794},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3887832462787628},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.3399568796157837},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.13576394319534302},{"id":"https://openalex.org/keywords/quadratically-constrained-quadratic-program","display_name":"Quadratically constrained quadratic program","score":0.13538077473640442},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.1333286464214325},{"id":"https://openalex.org/keywords/quadratic-programming","display_name":"Quadratic programming","score":0.08980056643486023}],"concepts":[{"id":"https://openalex.org/C50820777","wikidata":"https://www.wikidata.org/wiki/Q213723","display_name":"Hypercube","level":2,"score":0.839257538318634},{"id":"https://openalex.org/C101901036","wikidata":"https://www.wikidata.org/wiki/Q2269096","display_name":"Semidefinite programming","level":2,"score":0.7665145397186279},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7662174701690674},{"id":"https://openalex.org/C2778701210","wikidata":"https://www.wikidata.org/wiki/Q28130034","display_name":"Constructive","level":3,"score":0.6308352947235107},{"id":"https://openalex.org/C108710211","wikidata":"https://www.wikidata.org/wiki/Q11538","display_name":"Mathematical proof","level":2,"score":0.5029940009117126},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.48340168595314026},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.47940346598625183},{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.4481401741504669},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4466455578804016},{"id":"https://openalex.org/C206818286","wikidata":"https://www.wikidata.org/wiki/Q7449403","display_name":"Semidefinite embedding","level":4,"score":0.4309879541397095},{"id":"https://openalex.org/C147764199","wikidata":"https://www.wikidata.org/wiki/Q6865248","display_name":"Minification","level":2,"score":0.429604172706604},{"id":"https://openalex.org/C31170391","wikidata":"https://www.wikidata.org/wiki/Q188619","display_name":"Hierarchy","level":2,"score":0.42577847838401794},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3887832462787628},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3399568796157837},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.13576394319534302},{"id":"https://openalex.org/C65148998","wikidata":"https://www.wikidata.org/wiki/Q7268373","display_name":"Quadratically constrained quadratic program","level":3,"score":0.13538077473640442},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.1333286464214325},{"id":"https://openalex.org/C81845259","wikidata":"https://www.wikidata.org/wiki/Q290117","display_name":"Quadratic programming","level":2,"score":0.08980056643486023},{"id":"https://openalex.org/C98045186","wikidata":"https://www.wikidata.org/wiki/Q205663","display_name":"Process (computing)","level":2,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"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/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C34447519","wikidata":"https://www.wikidata.org/wiki/Q179522","display_name":"Market economy","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/100790835","is_oa":false,"landing_page_url":"https://doi.org/10.1137/100790835","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:oai:tilburguniversity.edu:publications/619d9658-77df-4b5e-9868-09aca0615347","is_oa":false,"landing_page_url":"https://research.tilburguniversity.edu/en/publications/619d9658-77df-4b5e-9868-09aca0615347","pdf_url":null,"source":{"id":"https://openalex.org/S4406923027","display_name":"Tilburg University Research Portal","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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"de Klerk, E & Laurent, M 2010, 'Error bounds for some semidefinite programming approaches to polynomial minimization on the hypercube', SIAM Journal on Optimization, vol. 20, no. 6, pp. 3104-3120. < http://dx.doi.org/10.1137/100790835 >","raw_type":"info:eu-repo/semantics/publishedVersion"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":29,"referenced_works":["https://openalex.org/W59386402","https://openalex.org/W99708544","https://openalex.org/W1518832340","https://openalex.org/W1783633569","https://openalex.org/W1967344706","https://openalex.org/W1970515840","https://openalex.org/W1985123706","https://openalex.org/W1996541174","https://openalex.org/W1997672673","https://openalex.org/W1999032440","https://openalex.org/W2001033871","https://openalex.org/W2017436952","https://openalex.org/W2037009101","https://openalex.org/W2047577886","https://openalex.org/W2081254453","https://openalex.org/W2083449425","https://openalex.org/W2092164538","https://openalex.org/W2094995801","https://openalex.org/W2105100124","https://openalex.org/W2114467398","https://openalex.org/W2114650657","https://openalex.org/W2126186592","https://openalex.org/W2133404041","https://openalex.org/W2133602590","https://openalex.org/W2137508197","https://openalex.org/W2138322123","https://openalex.org/W2165281529","https://openalex.org/W4254742099","https://openalex.org/W4255442211"],"related_works":["https://openalex.org/W2385886188","https://openalex.org/W2288891047","https://openalex.org/W2524928742","https://openalex.org/W2362452378","https://openalex.org/W2353517195","https://openalex.org/W3166939022","https://openalex.org/W1727084346","https://openalex.org/W2544939111","https://openalex.org/W2386048074","https://openalex.org/W2572095861"],"abstract_inverted_index":{"We":[0],"consider":[1],"the":[2,9,18,29,61],"problem":[3,26],"of":[4,20,31,47],"minimizing":[5],"a":[6],"polynomial":[7],"on":[8,60],"hypercube":[10],"$[0,1]^n$":[11],"and":[12,54],"derive":[13],"new":[14],"error":[15],"bounds":[16,56],"for":[17,57],"hierarchy":[19],"semidefinite":[21],"programming":[22],"approximations":[23,46],"to":[24,28],"this":[25],"corresponding":[27],"Positivstellensatz":[30],"Schm\u00fcdgen":[32],"[Math.":[33],"Ann.,":[34],"289":[35],"(1991),":[36],"pp.":[37],"203\u2013206].":[38],"The":[39],"main":[40],"tool":[41],"we":[42],"employ":[43],"is":[44],"Bernstein":[45],"polynomials,":[48],"which":[49],"also":[50],"gives":[51],"constructive":[52],"proofs":[53],"degree":[55],"positivity":[58],"certificates":[59],"hypercube.":[62]},"counts_by_year":[{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":4},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":7},{"year":2017,"cited_by_count":4},{"year":2016,"cited_by_count":4},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":9},{"year":2013,"cited_by_count":4},{"year":2012,"cited_by_count":3}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
