{"id":"https://openalex.org/W2135742226","doi":"https://doi.org/10.1109/acc.2007.4282347","title":"New Estimates for Practical Robust Negativity of Multilinear Functions","display_name":"New Estimates for Practical Robust Negativity of Multilinear Functions","publication_year":2007,"publication_date":"2007-07-01","ids":{"openalex":"https://openalex.org/W2135742226","doi":"https://doi.org/10.1109/acc.2007.4282347","mag":"2135742226"},"language":"en","primary_location":{"id":"doi:10.1109/acc.2007.4282347","is_oa":false,"landing_page_url":"https://doi.org/10.1109/acc.2007.4282347","pdf_url":null,"source":{"id":"https://openalex.org/S4210168941","display_name":"Proceedings of the ... American Control Conference/Proceedings of the American Control Conference","issn_l":"0743-1619","issn":["0743-1619","2378-5861"],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"conference"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2007 American Control Conference","raw_type":"proceedings-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/A5090622055","display_name":"Sheila R. Ross","orcid":null},"institutions":[{"id":"https://openalex.org/I135310074","display_name":"University of Wisconsin\u2013Madison","ror":"https://ror.org/01y2jtd41","country_code":"US","type":"education","lineage":["https://openalex.org/I135310074"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Sheila R. Ross","raw_affiliation_strings":["Department of Electrical and Computer Engineering, University of Wisconsin, Madison, USA","University of Wisconsin, Madison"],"affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering, University of Wisconsin, Madison, USA","institution_ids":["https://openalex.org/I135310074"]},{"raw_affiliation_string":"University of Wisconsin, Madison","institution_ids":["https://openalex.org/I135310074"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5054056783","display_name":"B. Ross Barmish","orcid":"https://orcid.org/0000-0002-2067-0349"},"institutions":[{"id":"https://openalex.org/I135310074","display_name":"University of Wisconsin\u2013Madison","ror":"https://ror.org/01y2jtd41","country_code":"US","type":"education","lineage":["https://openalex.org/I135310074"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"B. Ross Barmish","raw_affiliation_strings":["Department of Electrical and Computer Engineering, University of Wisconsin, Madison, USA","University of Wisconsin, Madison"],"affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering, University of Wisconsin, Madison, USA","institution_ids":["https://openalex.org/I135310074"]},{"raw_affiliation_string":"University of Wisconsin, Madison","institution_ids":["https://openalex.org/I135310074"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5090622055"],"corresponding_institution_ids":["https://openalex.org/I135310074"],"apc_list":null,"apc_paid":null,"fwci":0.6316,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.57446809,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"37","issue":null,"first_page":"5964","last_page":"5969"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9995999932289124,"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":0.9995999932289124,"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/T10928","display_name":"Probabilistic and Robust Engineering Design","score":0.9983999729156494,"subfield":{"id":"https://openalex.org/subfields/1804","display_name":"Statistics, Probability and Uncertainty"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T11697","display_name":"Numerical Methods and Algorithms","score":0.9958000183105469,"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/multilinear-map","display_name":"Multilinear map","score":0.9288604259490967},{"id":"https://openalex.org/keywords/negativity-effect","display_name":"Negativity effect","score":0.7033740282058716},{"id":"https://openalex.org/keywords/hypercube","display_name":"Hypercube","score":0.6089847087860107},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.5766066908836365},{"id":"https://openalex.org/keywords/relaxation","display_name":"Relaxation (psychology)","score":0.5402033925056458},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5187192559242249},{"id":"https://openalex.org/keywords/robustness","display_name":"Robustness (evolution)","score":0.4606251120567322},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.44457772374153137},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3633408546447754},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3525288701057434},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.32859086990356445},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.2766399681568146},{"id":"https://openalex.org/keywords/psychology","display_name":"Psychology","score":0.22496867179870605},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.14427077770233154},{"id":"https://openalex.org/keywords/cognitive-psychology","display_name":"Cognitive psychology","score":0.13436099886894226},{"id":"https://openalex.org/keywords/social-psychology","display_name":"Social psychology","score":0.119384765625}],"concepts":[{"id":"https://openalex.org/C84392682","wikidata":"https://www.wikidata.org/wiki/Q1952404","display_name":"Multilinear map","level":2,"score":0.9288604259490967},{"id":"https://openalex.org/C7453019","wikidata":"https://www.wikidata.org/wiki/Q16254302","display_name":"Negativity effect","level":2,"score":0.7033740282058716},{"id":"https://openalex.org/C50820777","wikidata":"https://www.wikidata.org/wiki/Q213723","display_name":"Hypercube","level":2,"score":0.6089847087860107},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.5766066908836365},{"id":"https://openalex.org/C2776029896","wikidata":"https://www.wikidata.org/wiki/Q3935810","display_name":"Relaxation (psychology)","level":2,"score":0.5402033925056458},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5187192559242249},{"id":"https://openalex.org/C63479239","wikidata":"https://www.wikidata.org/wiki/Q7353546","display_name":"Robustness (evolution)","level":3,"score":0.4606251120567322},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.44457772374153137},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3633408546447754},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3525288701057434},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.32859086990356445},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.2766399681568146},{"id":"https://openalex.org/C15744967","wikidata":"https://www.wikidata.org/wiki/Q9418","display_name":"Psychology","level":0,"score":0.22496867179870605},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.14427077770233154},{"id":"https://openalex.org/C180747234","wikidata":"https://www.wikidata.org/wiki/Q23373","display_name":"Cognitive psychology","level":1,"score":0.13436099886894226},{"id":"https://openalex.org/C77805123","wikidata":"https://www.wikidata.org/wiki/Q161272","display_name":"Social psychology","level":1,"score":0.119384765625},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"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/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/acc.2007.4282347","is_oa":false,"landing_page_url":"https://doi.org/10.1109/acc.2007.4282347","pdf_url":null,"source":{"id":"https://openalex.org/S4210168941","display_name":"Proceedings of the ... American Control Conference/Proceedings of the American Control Conference","issn_l":"0743-1619","issn":["0743-1619","2378-5861"],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"conference"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2007 American Control Conference","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.4000000059604645,"id":"https://metadata.un.org/sdg/10","display_name":"Reduced inequalities"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":19,"referenced_works":["https://openalex.org/W126279018","https://openalex.org/W1505281405","https://openalex.org/W1553318802","https://openalex.org/W1564380039","https://openalex.org/W1586428542","https://openalex.org/W1611766932","https://openalex.org/W1967184028","https://openalex.org/W1967344706","https://openalex.org/W2023169397","https://openalex.org/W2049087128","https://openalex.org/W2093368475","https://openalex.org/W2133838859","https://openalex.org/W2164090313","https://openalex.org/W2296319761","https://openalex.org/W2798735774","https://openalex.org/W4250589301","https://openalex.org/W4253174192","https://openalex.org/W6605086722","https://openalex.org/W6750414328"],"related_works":["https://openalex.org/W4318719034","https://openalex.org/W37958683","https://openalex.org/W1999178348","https://openalex.org/W2396820687","https://openalex.org/W4295021234","https://openalex.org/W3035010459","https://openalex.org/W4298178514","https://openalex.org/W4296311369","https://openalex.org/W3151212431","https://openalex.org/W2011892585"],"abstract_inverted_index":{"In":[0],"this":[1,49],"paper,":[2],"we":[3,44,54],"address":[4],"a":[5,17,27,46,70],"fundamental":[6],"NP-hard":[7],"problem":[8],"which":[9],"arises":[10],"in":[11,26,65],"many":[12],"application":[13],"areas:":[14],"Determine":[15],"whether":[16,58],"multilinear":[18],"function":[19],"f(x)":[20,59],"is":[21],"negative":[22,61],"for":[23,62],"all":[24,63],"x":[25,64],"hypercube":[28],"X.":[29],"Consistent":[30],"with":[31,35],"the":[32,36,41],"emerging":[33],"literature,":[34],"goal":[37],"being":[38],"to":[39,56],"reduce":[40],"computational":[42],"burden,":[43],"consider":[45],"relaxation":[47],"of":[48,72],"robust":[50],"negativity":[51],"problem.":[52],"Specifically,":[53],"seek":[55],"determine":[57],"remains":[60],"X":[66],"except":[67],"possibly":[68],"on":[69],"set":[71],"\"acceptably":[73],"small\"":[74],"volume.":[75]},"counts_by_year":[{"year":2013,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}