{"id":"https://openalex.org/W2153933553","doi":"https://doi.org/10.1109/acc.2006.1657280","title":"An algebraic geometry approach to nonlinear parametric optimization in control","display_name":"An algebraic geometry approach to nonlinear parametric optimization in control","publication_year":2006,"publication_date":"2006-01-01","ids":{"openalex":"https://openalex.org/W2153933553","doi":"https://doi.org/10.1109/acc.2006.1657280","mag":"2153933553"},"language":"en","primary_location":{"id":"doi:10.1109/acc.2006.1657280","is_oa":false,"landing_page_url":"https://doi.org/10.1109/acc.2006.1657280","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2006 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/A5075996296","display_name":"Ioannis A. Fotiou","orcid":null},"institutions":[{"id":"https://openalex.org/I35440088","display_name":"ETH Zurich","ror":"https://ror.org/05a28rw58","country_code":"CH","type":"education","lineage":["https://openalex.org/I2799323385","https://openalex.org/I35440088"]}],"countries":["CH"],"is_corresponding":false,"raw_author_name":"I.A. Fotiou","raw_affiliation_strings":["Automatic Control Laboratory, ETH Zurich, Zurich, Switzerland"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Automatic Control Laboratory, ETH Zurich, Zurich, Switzerland","institution_ids":["https://openalex.org/I35440088"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5011641162","display_name":"Philipp Rostalski","orcid":"https://orcid.org/0000-0003-0326-168X"},"institutions":[{"id":"https://openalex.org/I35440088","display_name":"ETH Zurich","ror":"https://ror.org/05a28rw58","country_code":"CH","type":"education","lineage":["https://openalex.org/I2799323385","https://openalex.org/I35440088"]}],"countries":["CH"],"is_corresponding":false,"raw_author_name":"P. Rostalski","raw_affiliation_strings":["Automatic Control Laboratory, ETH Zurich, Zurich, Switzerland"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Automatic Control Laboratory, ETH Zurich, Zurich, Switzerland","institution_ids":["https://openalex.org/I35440088"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5027670183","display_name":"Bernd Sturmfels","orcid":"https://orcid.org/0000-0002-6642-1479"},"institutions":[{"id":"https://openalex.org/I95457486","display_name":"University of California, Berkeley","ror":"https://ror.org/01an7q238","country_code":"US","type":"education","lineage":["https://openalex.org/I95457486"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"B. Sturmfels","raw_affiliation_strings":["Department of Mathematics, University of California Berkeley, CA, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of California Berkeley, CA, USA","institution_ids":["https://openalex.org/I95457486"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5025946191","display_name":"Manfred Morari","orcid":"https://orcid.org/0000-0002-7696-5058"},"institutions":[{"id":"https://openalex.org/I35440088","display_name":"ETH Zurich","ror":"https://ror.org/05a28rw58","country_code":"CH","type":"education","lineage":["https://openalex.org/I2799323385","https://openalex.org/I35440088"]}],"countries":["CH"],"is_corresponding":false,"raw_author_name":"M. Morari","raw_affiliation_strings":["Automatic Control Laboratory, ETH Zurich, Zurich, Switzerland"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Automatic Control Laboratory, ETH Zurich, Zurich, Switzerland","institution_ids":["https://openalex.org/I35440088"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":7.3446,"has_fulltext":false,"cited_by_count":19,"citation_normalized_percentile":{"value":0.96734976,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":null,"issue":null,"first_page":"6 pp.","last_page":"6 pp."},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10791","display_name":"Advanced Control Systems Optimization","score":0.9984999895095825,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10791","display_name":"Advanced Control Systems Optimization","score":0.9984999895095825,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11435","display_name":"Polynomial and algebraic computation","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/T11416","display_name":"Numerical methods for differential equations","score":0.9976000189781189,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/parametric-statistics","display_name":"Parametric statistics","score":0.6710786819458008},{"id":"https://openalex.org/keywords/gr\u00f6bner-basis","display_name":"Gr\u00f6bner basis","score":0.6086490154266357},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.5929287672042847},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.5679855346679688},{"id":"https://openalex.org/keywords/optimal-control","display_name":"Optimal control","score":0.5493561029434204},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5427168011665344},{"id":"https://openalex.org/keywords/optimization-problem","display_name":"Optimization problem","score":0.5065702199935913},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.49671298265457153},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.46118929982185364},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.4479213058948517},{"id":"https://openalex.org/keywords/algebraic-equation","display_name":"Algebraic equation","score":0.44326645135879517},{"id":"https://openalex.org/keywords/real-algebraic-geometry","display_name":"Real algebraic geometry","score":0.43541571497917175},{"id":"https://openalex.org/keywords/parametric-equation","display_name":"Parametric equation","score":0.41458866000175476},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.40601831674575806},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3946469724178314},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.34803637862205505},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.27334779500961304},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.20947489142417908},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.1782960295677185},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.14861583709716797}],"concepts":[{"id":"https://openalex.org/C117251300","wikidata":"https://www.wikidata.org/wiki/Q1849855","display_name":"Parametric statistics","level":2,"score":0.6710786819458008},{"id":"https://openalex.org/C198082693","wikidata":"https://www.wikidata.org/wiki/Q1551631","display_name":"Gr\u00f6bner basis","level":3,"score":0.6086490154266357},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.5929287672042847},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.5679855346679688},{"id":"https://openalex.org/C91575142","wikidata":"https://www.wikidata.org/wiki/Q1971426","display_name":"Optimal control","level":2,"score":0.5493561029434204},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5427168011665344},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.5065702199935913},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.49671298265457153},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.46118929982185364},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.4479213058948517},{"id":"https://openalex.org/C23917780","wikidata":"https://www.wikidata.org/wiki/Q50698","display_name":"Algebraic equation","level":3,"score":0.44326645135879517},{"id":"https://openalex.org/C2731732","wikidata":"https://www.wikidata.org/wiki/Q7301119","display_name":"Real algebraic geometry","level":3,"score":0.43541571497917175},{"id":"https://openalex.org/C99636146","wikidata":"https://www.wikidata.org/wiki/Q35889","display_name":"Parametric equation","level":2,"score":0.41458866000175476},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.40601831674575806},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3946469724178314},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.34803637862205505},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.27334779500961304},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.20947489142417908},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.1782960295677185},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.14861583709716797},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"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/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/acc.2006.1657280","is_oa":false,"landing_page_url":"https://doi.org/10.1109/acc.2006.1657280","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2006 American Control Conference","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":27,"referenced_works":["https://openalex.org/W22319829","https://openalex.org/W217710249","https://openalex.org/W268322338","https://openalex.org/W1483218536","https://openalex.org/W1487651112","https://openalex.org/W1539384849","https://openalex.org/W1588868664","https://openalex.org/W1605206672","https://openalex.org/W1967468346","https://openalex.org/W1977985274","https://openalex.org/W1985815049","https://openalex.org/W1993170675","https://openalex.org/W2016211524","https://openalex.org/W2073787051","https://openalex.org/W2094995801","https://openalex.org/W2116410324","https://openalex.org/W2125191920","https://openalex.org/W2133602590","https://openalex.org/W2153933553","https://openalex.org/W2162438491","https://openalex.org/W2296319761","https://openalex.org/W2962725330","https://openalex.org/W4250589301","https://openalex.org/W4292096448","https://openalex.org/W6608690752","https://openalex.org/W6635139765","https://openalex.org/W6646706800"],"related_works":["https://openalex.org/W3162124064","https://openalex.org/W2953857700","https://openalex.org/W2336285457","https://openalex.org/W72892335","https://openalex.org/W2117849070","https://openalex.org/W4238303259","https://openalex.org/W1500807497","https://openalex.org/W3157342981","https://openalex.org/W2366929179","https://openalex.org/W1525446462"],"abstract_inverted_index":{"We":[0],"present":[1],"a":[2,25],"method":[3,35,45],"for":[4,46],"nonlinear":[5],"parametric":[6],"optimization":[7,79],"based":[8],"on":[9],"algebraic":[10],"geometry.":[11],"The":[12,34],"problem":[13,80],"to":[14,23,31,71],"be":[15],"studied,":[16],"which":[17],"arises":[18],"in":[19,40,81],"optimal":[20],"control,":[21],"is":[22,69],"minimize":[24],"polynomial":[26,50],"function":[27],"with":[28,42],"parameters":[29],"subject":[30],"semialgebraic":[32],"constraints.":[33],"uses":[36],"Grobner":[37],"bases":[38],"computation":[39],"conjunction":[41],"the":[43,63,74,77],"eigenvalue":[44],"solving":[47],"systems":[48],"of":[49,76],"equations.":[51],"In":[52],"this":[53],"way,":[54],"certain":[55],"companion":[56],"matrices":[57],"are":[58],"constructed":[59],"off-line.":[60],"Then,":[61],"given":[62],"parameter":[64],"value,":[65],"an":[66],"on-line":[67],"algorithm":[68],"used":[70],"efficiently":[72],"obtain":[73],"optimizer":[75],"original":[78],"real":[82],"time":[83]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":4},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2016,"cited_by_count":3}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
