{"id":"https://openalex.org/W3175731276","doi":"https://doi.org/10.1137/21m1462568","title":"Algebraic Perspectives on Signomial Optimization","display_name":"Algebraic Perspectives on Signomial Optimization","publication_year":2022,"publication_date":"2022-12-15","ids":{"openalex":"https://openalex.org/W3175731276","doi":"https://doi.org/10.1137/21m1462568","mag":"3175731276"},"language":"en","primary_location":{"id":"doi:10.1137/21m1462568","is_oa":false,"landing_page_url":"https://doi.org/10.1137/21m1462568","pdf_url":null,"source":{"id":"https://openalex.org/S2996807011","display_name":"SIAM Journal on Applied Algebra and Geometry","issn_l":"2470-6566","issn":["2470-6566"],"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 Applied Algebra and Geometry","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/A5078197291","display_name":"Mareike Dressler","orcid":"https://orcid.org/0000-0002-5684-4101"},"institutions":[{"id":"https://openalex.org/I2803209242","display_name":"University of California System","ror":"https://ror.org/00pjdza24","country_code":"US","type":"education","lineage":["https://openalex.org/I2803209242"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Mareike Dressler","raw_affiliation_strings":["School of Mathematics and Statistics, University of New South Wales, Sydney, NSW 2052, Australia. Previously: Department of Mathematics, University of California, San Diego, La Jolla, CA 92093 USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, University of New South Wales, Sydney, NSW 2052, Australia. Previously: Department of Mathematics, University of California, San Diego, La Jolla, CA 92093 USA","institution_ids":["https://openalex.org/I2803209242"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5070917137","display_name":"Riley Murray","orcid":"https://orcid.org/0000-0003-1461-6458"},"institutions":[{"id":"https://openalex.org/I122411786","display_name":"California Institute of Technology","ror":"https://ror.org/05dxps055","country_code":"US","type":"education","lineage":["https://openalex.org/I122411786"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Riley Murray","raw_affiliation_strings":["Department of Electrical Engineering and Computer Sciences, University of California, Berkeley, CA 94720 USA. Previously: Department of Computing and Mathematical Sciences, California Institute of Technology, Pasadena, CA 91125 USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering and Computer Sciences, University of California, Berkeley, CA 94720 USA. Previously: Department of Computing and Mathematical Sciences, California Institute of Technology, Pasadena, CA 91125 USA","institution_ids":["https://openalex.org/I122411786"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.1879,"has_fulltext":false,"cited_by_count":7,"citation_normalized_percentile":{"value":0.84657948,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"6","issue":"4","first_page":"650","last_page":"684"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9991999864578247,"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":0.9991999864578247,"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/T10791","display_name":"Advanced Control Systems Optimization","score":0.9937999844551086,"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/T11053","display_name":"Process Optimization and Integration","score":0.9846000075340271,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8313428163528442},{"id":"https://openalex.org/keywords/convexity","display_name":"Convexity","score":0.5185337662696838},{"id":"https://openalex.org/keywords/hierarchy","display_name":"Hierarchy","score":0.438156396150589},{"id":"https://openalex.org/keywords/generalization","display_name":"Generalization","score":0.4295833706855774},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.4223973751068115},{"id":"https://openalex.org/keywords/relaxation","display_name":"Relaxation (psychology)","score":0.42230966687202454},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3378657102584839},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.11265495419502258}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8313428163528442},{"id":"https://openalex.org/C72134830","wikidata":"https://www.wikidata.org/wiki/Q5166524","display_name":"Convexity","level":2,"score":0.5185337662696838},{"id":"https://openalex.org/C31170391","wikidata":"https://www.wikidata.org/wiki/Q188619","display_name":"Hierarchy","level":2,"score":0.438156396150589},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.4295833706855774},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.4223973751068115},{"id":"https://openalex.org/C2776029896","wikidata":"https://www.wikidata.org/wiki/Q3935810","display_name":"Relaxation (psychology)","level":2,"score":0.42230966687202454},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3378657102584839},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.11265495419502258},{"id":"https://openalex.org/C15744967","wikidata":"https://www.wikidata.org/wiki/Q9418","display_name":"Psychology","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/C106159729","wikidata":"https://www.wikidata.org/wiki/Q2294553","display_name":"Financial economics","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},{"id":"https://openalex.org/C77805123","wikidata":"https://www.wikidata.org/wiki/Q161272","display_name":"Social psychology","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/21m1462568","is_oa":false,"landing_page_url":"https://doi.org/10.1137/21m1462568","pdf_url":null,"source":{"id":"https://openalex.org/S2996807011","display_name":"SIAM Journal on Applied Algebra and Geometry","issn_l":"2470-6566","issn":["2470-6566"],"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 Applied Algebra and Geometry","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":82,"referenced_works":["https://openalex.org/W657882497","https://openalex.org/W1451881698","https://openalex.org/W1482962557","https://openalex.org/W1569685525","https://openalex.org/W1632601927","https://openalex.org/W1967344706","https://openalex.org/W1968557508","https://openalex.org/W1972537951","https://openalex.org/W1974915811","https://openalex.org/W1982292900","https://openalex.org/W1982433837","https://openalex.org/W1988059449","https://openalex.org/W1989190791","https://openalex.org/W2002713832","https://openalex.org/W2014328192","https://openalex.org/W2021674665","https://openalex.org/W2032362434","https://openalex.org/W2037009101","https://openalex.org/W2043653908","https://openalex.org/W2050339136","https://openalex.org/W2051572921","https://openalex.org/W2053272802","https://openalex.org/W2057009136","https://openalex.org/W2072273382","https://openalex.org/W2077162779","https://openalex.org/W2079135578","https://openalex.org/W2090967418","https://openalex.org/W2092235931","https://openalex.org/W2101538582","https://openalex.org/W2108380721","https://openalex.org/W2117127754","https://openalex.org/W2119360871","https://openalex.org/W2133404041","https://openalex.org/W2137801186","https://openalex.org/W2146914168","https://openalex.org/W2166798101","https://openalex.org/W2216668975","https://openalex.org/W2239251014","https://openalex.org/W2271851628","https://openalex.org/W2296530532","https://openalex.org/W2320769111","https://openalex.org/W2321429733","https://openalex.org/W2516653421","https://openalex.org/W2799036797","https://openalex.org/W2810989255","https://openalex.org/W2889726166","https://openalex.org/W2894531996","https://openalex.org/W2895618514","https://openalex.org/W2907008276","https://openalex.org/W2911427463","https://openalex.org/W2944874335","https://openalex.org/W2950353857","https://openalex.org/W2950530938","https://openalex.org/W2955472196","https://openalex.org/W2959479683","https://openalex.org/W2962700275","https://openalex.org/W2963917343","https://openalex.org/W2963968845","https://openalex.org/W2964069080","https://openalex.org/W2966968005","https://openalex.org/W2997618127","https://openalex.org/W3006858192","https://openalex.org/W3009816526","https://openalex.org/W3023950925","https://openalex.org/W3083505422","https://openalex.org/W3084445672","https://openalex.org/W3092934452","https://openalex.org/W3095553164","https://openalex.org/W3096619564","https://openalex.org/W3100197943","https://openalex.org/W3101637132","https://openalex.org/W3103140205","https://openalex.org/W3113077080","https://openalex.org/W3119965387","https://openalex.org/W3120760274","https://openalex.org/W3129955648","https://openalex.org/W3133541217","https://openalex.org/W3137973502","https://openalex.org/W3151600232","https://openalex.org/W3203920743","https://openalex.org/W4233154616","https://openalex.org/W4296788127"],"related_works":["https://openalex.org/W2187391117","https://openalex.org/W1981809986","https://openalex.org/W1843467136","https://openalex.org/W2949367465","https://openalex.org/W4235203617","https://openalex.org/W2006359264","https://openalex.org/W3029201158","https://openalex.org/W2056357792","https://openalex.org/W2051545453","https://openalex.org/W4299607453"],"abstract_inverted_index":{".Signomials":[0],"are":[1],"obtained":[2],"by":[3,88],"generalizing":[4],"polynomials":[5],"to":[6,30,48,130,196],"allow":[7],"for":[8,59,160,168],"arbitrary":[9],"real":[10],"exponents.":[11],"This":[12],"generalization":[13],"offers":[14],"great":[15],"expressive":[16],"power":[17],"but":[18],"has":[19],"historically":[20],"sacrificed":[21],"the":[22,40,73,78,95,110,139,174,190],"organizing":[23],"principle":[24,37],"of":[25,42,54,64,80,94,100,112,146,149,173,177,194,200,213],"\"degree\"":[26],"that":[27,36,183],"is":[28],"central":[29],"polynomial":[31],"optimization":[32,61],"theory.":[33],"We":[34],"reclaim":[35],"here":[38],"through":[39],"concept":[41,79],"signomial":[43,60,103,161,197],"rings,":[44],"which":[45],"we":[46,108,185],"use":[47],"derive":[49],"complete":[50],"convex":[51],"relaxation":[52],"hierarchies":[53],"upper":[55,150],"and":[56,83,123,136,138,192],"lower":[57,74],"bounds":[58,75,151],"via":[62],"sums":[63],"arithmetic-geometric":[65,201],"exponentials":[66],"(SAGE)":[67],"nonnegativity":[68,162],"certificates.":[69],"The":[70,144],"Positivstellensatz":[71,159],"underlying":[72],"relies":[76],"on":[77,189],"conditional":[81],"SAGE":[82],"removes":[84],"regularity":[85],"conditions":[86],"required":[87],"earlier":[89],"works,":[90],"such":[91,117],"as":[92,118],"convexity":[93],"feasible":[96],"set":[97,166],"or":[98],"Archimedeanity":[99],"its":[101],"representing":[102],"inequalities.":[104],"Through":[105],"worked":[106],"examples":[107,127],"illustrate":[109],"practicality":[111],"this":[113],"hierarchy":[114,141,148],"in":[115],"areas":[116],"chemical":[119,124],"reaction":[120],"network":[121],"theory":[122],"engineering.":[125],"These":[126],"include":[128],"comparisons":[129],"direct":[131],"global":[132],"solvers":[133],"(e.g.,":[134],"BARON":[135],"ANTIGONE)":[137],"Lasserre":[140],"(where":[142],"appropriate).":[143],"completeness":[145],"our":[147],"follows":[152],"from":[153],"a":[154,158,164],"generic":[155],"construction":[156],"whereby":[157],"over":[163],"compact":[165],"provides":[167],"arbitrarily":[169],"strong":[170],"outer":[171],"approximations":[172],"corresponding":[175],"cone":[176,208],"nonnegative":[178],"signomials.":[179],"While":[180],"working":[181],"toward":[182],"result,":[184],"prove":[186],"basic":[187],"facts":[188],"existence":[191],"uniqueness":[193],"solutions":[195],"moment":[198],"problems.Keywordssums":[199],"exponentialsnonnegative":[202],"signomialsexponential":[203],"sumssignomial":[204],"programmingrelative":[205],"entropy":[206],"programmingexponential":[207],"programmingmoment":[209],"problemsnonnegative":[210],"circuit":[211],"polynomialssums":[212],"squarespolynomial":[214],"optimizationMSC":[215],"codes14P9990C2590C2352A2028B15":[216]},"counts_by_year":[{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
