{"id":"https://openalex.org/W2771160919","doi":"https://doi.org/10.1137/17m1160124","title":"Sum-of-Squares Optimization without Semidefinite Programming","display_name":"Sum-of-Squares Optimization without Semidefinite Programming","publication_year":2019,"publication_date":"2019-01-01","ids":{"openalex":"https://openalex.org/W2771160919","doi":"https://doi.org/10.1137/17m1160124","mag":"2771160919"},"language":"en","primary_location":{"id":"doi:10.1137/17m1160124","is_oa":false,"landing_page_url":"https://doi.org/10.1137/17m1160124","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":"preprint","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1712.01792","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5058400272","display_name":"D\u00e1vid Papp","orcid":"https://orcid.org/0000-0003-4498-6417"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"D\u00e1vid Papp","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5072911430","display_name":"Sercan Y\u0131ld\u0131z","orcid":"https://orcid.org/0000-0003-2004-1101"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Sercan Yildiz","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.3245,"has_fulltext":true,"cited_by_count":3,"citation_normalized_percentile":{"value":0.48816364,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"29","issue":"1","first_page":"822","last_page":"851"},"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/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9926000237464905,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"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/T10792","display_name":"Matrix Theory and Algorithms","score":0.9865999817848206,"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/semidefinite-programming","display_name":"Semidefinite programming","score":0.9318526983261108},{"id":"https://openalex.org/keywords/conic-optimization","display_name":"Conic optimization","score":0.7643923163414001},{"id":"https://openalex.org/keywords/semidefinite-embedding","display_name":"Semidefinite embedding","score":0.6834801435470581},{"id":"https://openalex.org/keywords/explained-sum-of-squares","display_name":"Explained sum of squares","score":0.6308539509773254},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6237432956695557},{"id":"https://openalex.org/keywords/interior-point-method","display_name":"Interior point method","score":0.6087996363639832},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5860516428947449},{"id":"https://openalex.org/keywords/second-order-cone-programming","display_name":"Second-order cone programming","score":0.5789989829063416},{"id":"https://openalex.org/keywords/conic-section","display_name":"Conic section","score":0.5306274890899658},{"id":"https://openalex.org/keywords/quadratically-constrained-quadratic-program","display_name":"Quadratically constrained quadratic program","score":0.5256556272506714},{"id":"https://openalex.org/keywords/least-squares-function-approximation","display_name":"Least-squares function approximation","score":0.44666630029678345},{"id":"https://openalex.org/keywords/linear-programming","display_name":"Linear programming","score":0.4270366430282593},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3408512771129608},{"id":"https://openalex.org/keywords/quadratic-programming","display_name":"Quadratic programming","score":0.27170097827911377},{"id":"https://openalex.org/keywords/convex-optimization","display_name":"Convex optimization","score":0.1318415105342865},{"id":"https://openalex.org/keywords/subderivative","display_name":"Subderivative","score":0.09689411520957947}],"concepts":[{"id":"https://openalex.org/C101901036","wikidata":"https://www.wikidata.org/wiki/Q2269096","display_name":"Semidefinite programming","level":2,"score":0.9318526983261108},{"id":"https://openalex.org/C79187972","wikidata":"https://www.wikidata.org/wiki/Q2654791","display_name":"Conic optimization","level":5,"score":0.7643923163414001},{"id":"https://openalex.org/C206818286","wikidata":"https://www.wikidata.org/wiki/Q7449403","display_name":"Semidefinite embedding","level":4,"score":0.6834801435470581},{"id":"https://openalex.org/C49847556","wikidata":"https://www.wikidata.org/wiki/Q3964631","display_name":"Explained sum of squares","level":2,"score":0.6308539509773254},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6237432956695557},{"id":"https://openalex.org/C155253501","wikidata":"https://www.wikidata.org/wiki/Q461992","display_name":"Interior point method","level":2,"score":0.6087996363639832},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5860516428947449},{"id":"https://openalex.org/C111397411","wikidata":"https://www.wikidata.org/wiki/Q7442977","display_name":"Second-order cone programming","level":4,"score":0.5789989829063416},{"id":"https://openalex.org/C108598597","wikidata":"https://www.wikidata.org/wiki/Q124255","display_name":"Conic section","level":2,"score":0.5306274890899658},{"id":"https://openalex.org/C65148998","wikidata":"https://www.wikidata.org/wiki/Q7268373","display_name":"Quadratically constrained quadratic program","level":3,"score":0.5256556272506714},{"id":"https://openalex.org/C9936470","wikidata":"https://www.wikidata.org/wiki/Q6510405","display_name":"Least-squares function approximation","level":3,"score":0.44666630029678345},{"id":"https://openalex.org/C41045048","wikidata":"https://www.wikidata.org/wiki/Q202843","display_name":"Linear programming","level":2,"score":0.4270366430282593},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3408512771129608},{"id":"https://openalex.org/C81845259","wikidata":"https://www.wikidata.org/wiki/Q290117","display_name":"Quadratic programming","level":2,"score":0.27170097827911377},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.1318415105342865},{"id":"https://openalex.org/C200661725","wikidata":"https://www.wikidata.org/wiki/Q289500","display_name":"Subderivative","level":4,"score":0.09689411520957947},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"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/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1137/17m1160124","is_oa":false,"landing_page_url":"https://doi.org/10.1137/17m1160124","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:arXiv.org:1712.01792","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1712.01792","pdf_url":"https://arxiv.org/pdf/1712.01792","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"text"},{"id":"mag:2771160919","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1712.01792.pdf","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},{"id":"doi:10.48550/arxiv.1712.01792","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1712.01792","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1712.01792","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1712.01792","pdf_url":"https://arxiv.org/pdf/1712.01792","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"text"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2067228889","display_name":null,"funder_award_id":"DMS-1719828","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G3561834706","display_name":null,"funder_award_id":"DMS-1638521","funder_id":"https://openalex.org/F4320337380","funder_display_name":"Division of Mathematical Sciences"},{"id":"https://openalex.org/G4604692985","display_name":"Statistical and Applied Mathematical Sciences Institute","funder_award_id":"1638521","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G5963970009","display_name":null,"funder_award_id":"DMS-1638521","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G5985085362","display_name":null,"funder_award_id":"1638521","funder_id":"https://openalex.org/F4320337380","funder_display_name":"Division of Mathematical Sciences"},{"id":"https://openalex.org/G7504265569","display_name":"Practical Large-Scale Sum-of-Squares Optimization","funder_award_id":"1719828","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320337380","display_name":"Division of Mathematical Sciences","ror":"https://ror.org/051fftw81"}],"has_content":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W2771160919.pdf"},"referenced_works_count":55,"referenced_works":["https://openalex.org/W21639112","https://openalex.org/W99708544","https://openalex.org/W253307310","https://openalex.org/W622930292","https://openalex.org/W1536262233","https://openalex.org/W1592751003","https://openalex.org/W1632601927","https://openalex.org/W1967073510","https://openalex.org/W1967344706","https://openalex.org/W1995320256","https://openalex.org/W1999613943","https://openalex.org/W1999913571","https://openalex.org/W2001033871","https://openalex.org/W2001371760","https://openalex.org/W2005482089","https://openalex.org/W2021790426","https://openalex.org/W2030072108","https://openalex.org/W2037009101","https://openalex.org/W2048552622","https://openalex.org/W2049049772","https://openalex.org/W2050724454","https://openalex.org/W2055993677","https://openalex.org/W2056984789","https://openalex.org/W2058404049","https://openalex.org/W2059998776","https://openalex.org/W2061293389","https://openalex.org/W2077924482","https://openalex.org/W2078574976","https://openalex.org/W2082037093","https://openalex.org/W2082089361","https://openalex.org/W2085850581","https://openalex.org/W2091354775","https://openalex.org/W2092808221","https://openalex.org/W2101504517","https://openalex.org/W2104842300","https://openalex.org/W2109990880","https://openalex.org/W2114408464","https://openalex.org/W2114467398","https://openalex.org/W2118310633","https://openalex.org/W2133404041","https://openalex.org/W2142370198","https://openalex.org/W2152345982","https://openalex.org/W2156825077","https://openalex.org/W2165323796","https://openalex.org/W2166798101","https://openalex.org/W2170721105","https://openalex.org/W2296543004","https://openalex.org/W2529726785","https://openalex.org/W2593062745","https://openalex.org/W2773474135","https://openalex.org/W2795779869","https://openalex.org/W2964111768","https://openalex.org/W3148725352","https://openalex.org/W4254742099","https://openalex.org/W4255442211"],"related_works":["https://openalex.org/W111161418","https://openalex.org/W2061607408","https://openalex.org/W1986699627","https://openalex.org/W2743085740","https://openalex.org/W2033005587","https://openalex.org/W1992459686","https://openalex.org/W152698231","https://openalex.org/W2394710522","https://openalex.org/W3012257151","https://openalex.org/W1623728894","https://openalex.org/W1971195964","https://openalex.org/W3154076173","https://openalex.org/W3105236435","https://openalex.org/W2288470313","https://openalex.org/W2482087498","https://openalex.org/W2018204628","https://openalex.org/W2991461359","https://openalex.org/W2028522687","https://openalex.org/W3154036230","https://openalex.org/W2268876679"],"abstract_inverted_index":{"We":[0],"propose":[1],"a":[2,40,55],"homogeneous":[3],"primal-dual":[4],"interior-point":[5],"method":[6,102],"to":[7,85],"solve":[8],"sum-of-squares":[9,27,50,118],"optimization":[10,16,114],"problems":[11,115],"by":[12],"combining":[13],"nonsymmetric":[14],"conic":[15],"techniques":[17],"and":[18,29,63],"polynomial":[19],"interpolation.":[20],"The":[21],"approach":[22,70,77,112],"optimizes":[23],"directly":[24],"over":[25,116],"the":[26,33,47,67,72,79,86,100,110],"cone":[28],"its":[30],"dual,":[31],"circumventing":[32],"semidefinite":[34,87],"programming":[35],"(SDP)":[36],"reformulation,":[37,81],"which":[38],"requires":[39],"large":[41],"number":[42],"of":[43,49,106],"auxiliary":[44],"variables":[45],"when":[46],"degree":[48,73],"polynomials":[51],"is":[52,103],"large.":[53],"As":[54],"result,":[56],"it":[57],"has":[58],"substantially":[59],"lower":[60],"theoretical":[61],"time":[62],"space":[64],"complexity":[65],"than":[66,109],"conventional":[68],"SDP-based":[69,111],"as":[71],"increases.":[74],"Although":[75],"our":[76],"avoids":[78],"SDP":[80],"an":[82],"optimal":[83],"solution":[84],"program":[88],"can":[89],"be":[90],"recovered":[91],"with":[92],"little":[93],"additional":[94],"effort.":[95],"Computational":[96],"results":[97],"confirm":[98],"that":[99],"proposed":[101],"several":[104],"orders":[105],"magnitude":[107],"faster":[108],"for":[113],"high-degree":[117],"polynomials.":[119]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1}],"updated_date":"2026-06-22T08:00:12.763002","created_date":"2025-10-10T00:00:00"}