{"id":"https://openalex.org/W2049629624","doi":"https://doi.org/10.1145/2465506.2466575","title":"Convex algebraic geometry and semidefinite optimization","display_name":"Convex algebraic geometry and semidefinite optimization","publication_year":2013,"publication_date":"2013-06-25","ids":{"openalex":"https://openalex.org/W2049629624","doi":"https://doi.org/10.1145/2465506.2466575","mag":"2049629624"},"language":"en","primary_location":{"id":"doi:10.1145/2465506.2466575","is_oa":false,"landing_page_url":"https://doi.org/10.1145/2465506.2466575","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 38th International Symposium on Symbolic and Algebraic Computation","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/A5031935416","display_name":"Pablo A. Parrilo","orcid":"https://orcid.org/0000-0003-1132-8477"},"institutions":[{"id":"https://openalex.org/I63966007","display_name":"Massachusetts Institute of Technology","ror":"https://ror.org/042nb2s44","country_code":"US","type":"education","lineage":["https://openalex.org/I63966007"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Pablo A. Parrilo","raw_affiliation_strings":["Massachusetts Institute of Technology, Cambridge, MA, USA","Massachusetts Institute of Technology; ,; Cambridge MA USA"],"affiliations":[{"raw_affiliation_string":"Massachusetts Institute of Technology, Cambridge, MA, USA","institution_ids":["https://openalex.org/I63966007"]},{"raw_affiliation_string":"Massachusetts Institute of Technology; ,; Cambridge MA USA","institution_ids":["https://openalex.org/I63966007"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5031935416"],"corresponding_institution_ids":["https://openalex.org/I63966007"],"apc_list":null,"apc_paid":null,"fwci":1.31226727,"has_fulltext":false,"cited_by_count":8,"citation_normalized_percentile":{"value":0.80545599,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":null,"issue":null,"first_page":"9","last_page":"10"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9998999834060669,"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":0.9998999834060669,"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/T11435","display_name":"Polynomial and algebraic computation","score":0.9987000226974487,"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/T11697","display_name":"Numerical Methods and Algorithms","score":0.9958999752998352,"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/real-algebraic-geometry","display_name":"Real algebraic geometry","score":0.7095583081245422},{"id":"https://openalex.org/keywords/convexity","display_name":"Convexity","score":0.7015894651412964},{"id":"https://openalex.org/keywords/intersection","display_name":"Intersection (aeronautics)","score":0.615642249584198},{"id":"https://openalex.org/keywords/convex-geometry","display_name":"Convex geometry","score":0.5713597536087036},{"id":"https://openalex.org/keywords/algebraic-geometry","display_name":"Algebraic geometry","score":0.5255531072616577},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.5201970934867859},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5133621096611023},{"id":"https://openalex.org/keywords/convex-optimization","display_name":"Convex optimization","score":0.5111103653907776},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.4995863437652588},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.4927361309528351},{"id":"https://openalex.org/keywords/algebraic-surface","display_name":"Algebraic surface","score":0.49074041843414307},{"id":"https://openalex.org/keywords/convex-analysis","display_name":"Convex analysis","score":0.4616381824016571},{"id":"https://openalex.org/keywords/function-field-of-an-algebraic-variety","display_name":"Function field of an algebraic variety","score":0.4426562786102295},{"id":"https://openalex.org/keywords/conic-optimization","display_name":"Conic optimization","score":0.4329671561717987},{"id":"https://openalex.org/keywords/tropical-geometry","display_name":"Tropical geometry","score":0.41718408465385437},{"id":"https://openalex.org/keywords/differential-algebraic-geometry","display_name":"Differential algebraic geometry","score":0.415729284286499},{"id":"https://openalex.org/keywords/dimension-of-an-algebraic-variety","display_name":"Dimension of an algebraic variety","score":0.41462987661361694},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.381415992975235},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.28008612990379333},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.26097214221954346},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.12163171172142029}],"concepts":[{"id":"https://openalex.org/C2731732","wikidata":"https://www.wikidata.org/wiki/Q7301119","display_name":"Real algebraic geometry","level":3,"score":0.7095583081245422},{"id":"https://openalex.org/C72134830","wikidata":"https://www.wikidata.org/wiki/Q5166524","display_name":"Convexity","level":2,"score":0.7015894651412964},{"id":"https://openalex.org/C64543145","wikidata":"https://www.wikidata.org/wiki/Q162942","display_name":"Intersection (aeronautics)","level":2,"score":0.615642249584198},{"id":"https://openalex.org/C110202963","wikidata":"https://www.wikidata.org/wiki/Q1783542","display_name":"Convex geometry","level":5,"score":0.5713597536087036},{"id":"https://openalex.org/C68363185","wikidata":"https://www.wikidata.org/wiki/Q180969","display_name":"Algebraic geometry","level":2,"score":0.5255531072616577},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.5201970934867859},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5133621096611023},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.5111103653907776},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.4995863437652588},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.4927361309528351},{"id":"https://openalex.org/C69653121","wikidata":"https://www.wikidata.org/wiki/Q1434805","display_name":"Algebraic surface","level":3,"score":0.49074041843414307},{"id":"https://openalex.org/C12108790","wikidata":"https://www.wikidata.org/wiki/Q2234833","display_name":"Convex analysis","level":4,"score":0.4616381824016571},{"id":"https://openalex.org/C10996884","wikidata":"https://www.wikidata.org/wiki/Q5508773","display_name":"Function field of an algebraic variety","level":3,"score":0.4426562786102295},{"id":"https://openalex.org/C79187972","wikidata":"https://www.wikidata.org/wiki/Q2654791","display_name":"Conic optimization","level":5,"score":0.4329671561717987},{"id":"https://openalex.org/C202652594","wikidata":"https://www.wikidata.org/wiki/Q2982669","display_name":"Tropical geometry","level":2,"score":0.41718408465385437},{"id":"https://openalex.org/C26959085","wikidata":"https://www.wikidata.org/wiki/Q5275330","display_name":"Differential algebraic geometry","level":5,"score":0.415729284286499},{"id":"https://openalex.org/C25971838","wikidata":"https://www.wikidata.org/wiki/Q5277261","display_name":"Dimension of an algebraic variety","level":3,"score":0.41462987661361694},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.381415992975235},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.28008612990379333},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.26097214221954346},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.12163171172142029},{"id":"https://openalex.org/C146978453","wikidata":"https://www.wikidata.org/wiki/Q3798668","display_name":"Aerospace engineering","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/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.0},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.0},{"id":"https://openalex.org/C186219872","wikidata":"https://www.wikidata.org/wiki/Q955889","display_name":"Differential algebraic equation","level":4,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C106159729","wikidata":"https://www.wikidata.org/wiki/Q2294553","display_name":"Financial economics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1145/2465506.2466575","is_oa":false,"landing_page_url":"https://doi.org/10.1145/2465506.2466575","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 38th International Symposium on Symbolic and Algebraic Computation","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":12,"referenced_works":["https://openalex.org/W653291882","https://openalex.org/W1806104592","https://openalex.org/W1967184028","https://openalex.org/W1967344706","https://openalex.org/W1989190791","https://openalex.org/W1995320256","https://openalex.org/W2049087128","https://openalex.org/W2055993677","https://openalex.org/W2133404041","https://openalex.org/W2146586176","https://openalex.org/W3144358832","https://openalex.org/W4236743822"],"related_works":["https://openalex.org/W2032847817","https://openalex.org/W2170846659","https://openalex.org/W3133654707","https://openalex.org/W415152954","https://openalex.org/W2183851690","https://openalex.org/W1769917728","https://openalex.org/W4394667671","https://openalex.org/W2962680152","https://openalex.org/W2506747709","https://openalex.org/W2553268629"],"abstract_inverted_index":{"In":[0],"the":[1,31,36,49,76],"past":[2],"decade":[3],"there":[4],"has":[5,95],"been":[6],"a":[7,60,64],"surge":[8],"of":[9,33,42,45,51,78],"interest":[10],"in":[11,26],"algebraic":[12,46,79,100],"approaches":[13],"to":[14,75],"optimization":[15],"problems":[16],"defined":[17],"by":[18],"multivariate":[19],"polynomials.":[20],"Fundamental":[21],"mathematical":[22],"challenges":[23],"that":[24],"arise":[25],"this":[27],"area":[28,94],"include":[29],"understanding":[30],"structure":[32],"nonnegative":[34],"polynomials,":[35],"interplay":[37],"between":[38],"efficiency":[39],"and":[40,48,55,63,82,90],"complexity":[41],"different":[43],"representations":[44],"sets,":[47],"development":[50],"effective":[52],"algorithms.":[53],"Remarkably,":[54],"perhaps":[56],"unexpectedly,":[57],"convexity":[58],"provides":[59],"new":[61],"viewpoint":[62],"powerful":[65],"framework":[66],"for":[67],"addressing":[68],"these":[69],"questions.":[70],"This":[71,92],"naturally":[72],"brings":[73],"us":[74],"intersection":[77],"geometry,":[80,84],"optimization,":[81],"convex":[83,99],"with":[85],"an":[86],"emphasis":[87],"on":[88],"algorithms":[89],"computation.":[91],"emerging":[93],"become":[96],"known":[97],"as":[98],"geometry.":[101]},"counts_by_year":[{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
