{"id":"https://openalex.org/W4402307095","doi":"https://doi.org/10.1007/s12532-024-00264-w","title":"Solving clustered low-rank semidefinite programs arising from polynomial optimization","display_name":"Solving clustered low-rank semidefinite programs arising from polynomial optimization","publication_year":2024,"publication_date":"2024-09-01","ids":{"openalex":"https://openalex.org/W4402307095","doi":"https://doi.org/10.1007/s12532-024-00264-w"},"language":"en","primary_location":{"id":"doi:10.1007/s12532-024-00264-w","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s12532-024-00264-w","pdf_url":"https://link.springer.com/content/pdf/10.1007/s12532-024-00264-w.pdf","source":{"id":"https://openalex.org/S173077093","display_name":"Mathematical Programming Computation","issn_l":"1867-2949","issn":["1867-2949","1867-2957"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematical Programming Computation","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s12532-024-00264-w.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5060251834","display_name":"Nando Leijenhorst","orcid":null},"institutions":[{"id":"https://openalex.org/I98358874","display_name":"Delft University of Technology","ror":"https://ror.org/02e2c7k09","country_code":"NL","type":"education","lineage":["https://openalex.org/I98358874"]}],"countries":["NL"],"is_corresponding":true,"raw_author_name":"Nando Leijenhorst","raw_affiliation_strings":["Delft University of Technology, Mekelweg 4, 2628 CD, Delft, The Netherlands"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Delft University of Technology, Mekelweg 4, 2628 CD, Delft, The Netherlands","institution_ids":["https://openalex.org/I98358874"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5061628061","display_name":"David de Laat","orcid":"https://orcid.org/0000-0002-5178-1906"},"institutions":[{"id":"https://openalex.org/I98358874","display_name":"Delft University of Technology","ror":"https://ror.org/02e2c7k09","country_code":"NL","type":"education","lineage":["https://openalex.org/I98358874"]}],"countries":["NL"],"is_corresponding":false,"raw_author_name":"David de Laat","raw_affiliation_strings":["Delft University of Technology, Mekelweg 4, 2628 CD, Delft, The Netherlands"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Delft University of Technology, Mekelweg 4, 2628 CD, Delft, The Netherlands","institution_ids":["https://openalex.org/I98358874"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5060251834"],"corresponding_institution_ids":["https://openalex.org/I98358874"],"apc_list":{"value":2390,"currency":"EUR","value_usd":3090},"apc_paid":{"value":2390,"currency":"EUR","value_usd":3090},"fwci":3.3814,"has_fulltext":true,"cited_by_count":5,"citation_normalized_percentile":{"value":0.92653233,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"16","issue":"3","first_page":"503","last_page":"534"},"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":0.9991999864578247,"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/T11697","display_name":"Numerical Methods and Algorithms","score":0.9968000054359436,"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":0.6687437891960144},{"id":"https://openalex.org/keywords/theory-of-computation","display_name":"Theory of computation","score":0.6327974796295166},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.5951024293899536},{"id":"https://openalex.org/keywords/speedup","display_name":"Speedup","score":0.5727864503860474},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5497543811798096},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.5191166400909424},{"id":"https://openalex.org/keywords/rank","display_name":"Rank (graph theory)","score":0.4862586259841919},{"id":"https://openalex.org/keywords/interior-point-method","display_name":"Interior point method","score":0.4733726382255554},{"id":"https://openalex.org/keywords/reduction","display_name":"Reduction (mathematics)","score":0.4673875570297241},{"id":"https://openalex.org/keywords/sampling","display_name":"Sampling (signal processing)","score":0.43507251143455505},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.43376830220222473},{"id":"https://openalex.org/keywords/binary-number","display_name":"Binary number","score":0.42978692054748535},{"id":"https://openalex.org/keywords/condition-number","display_name":"Condition number","score":0.4286591410636902},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.41683048009872437},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.4145854115486145},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.37689119577407837},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.36057019233703613},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.30863574147224426},{"id":"https://openalex.org/keywords/filter","display_name":"Filter (signal processing)","score":0.10186576843261719},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.0959109365940094},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.08368262648582458}],"concepts":[{"id":"https://openalex.org/C101901036","wikidata":"https://www.wikidata.org/wiki/Q2269096","display_name":"Semidefinite programming","level":2,"score":0.6687437891960144},{"id":"https://openalex.org/C24858836","wikidata":"https://www.wikidata.org/wiki/Q844718","display_name":"Theory of computation","level":2,"score":0.6327974796295166},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.5951024293899536},{"id":"https://openalex.org/C68339613","wikidata":"https://www.wikidata.org/wiki/Q1549489","display_name":"Speedup","level":2,"score":0.5727864503860474},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5497543811798096},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.5191166400909424},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.4862586259841919},{"id":"https://openalex.org/C155253501","wikidata":"https://www.wikidata.org/wiki/Q461992","display_name":"Interior point method","level":2,"score":0.4733726382255554},{"id":"https://openalex.org/C111335779","wikidata":"https://www.wikidata.org/wiki/Q3454686","display_name":"Reduction (mathematics)","level":2,"score":0.4673875570297241},{"id":"https://openalex.org/C140779682","wikidata":"https://www.wikidata.org/wiki/Q210868","display_name":"Sampling (signal processing)","level":3,"score":0.43507251143455505},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.43376830220222473},{"id":"https://openalex.org/C48372109","wikidata":"https://www.wikidata.org/wiki/Q3913","display_name":"Binary number","level":2,"score":0.42978692054748535},{"id":"https://openalex.org/C84545080","wikidata":"https://www.wikidata.org/wiki/Q1147936","display_name":"Condition number","level":3,"score":0.4286591410636902},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.41683048009872437},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4145854115486145},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.37689119577407837},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.36057019233703613},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.30863574147224426},{"id":"https://openalex.org/C106131492","wikidata":"https://www.wikidata.org/wiki/Q3072260","display_name":"Filter (signal processing)","level":2,"score":0.10186576843261719},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0959109365940094},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.08368262648582458},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.0},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.0},{"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/C31972630","wikidata":"https://www.wikidata.org/wiki/Q844240","display_name":"Computer vision","level":1,"score":0.0},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s12532-024-00264-w","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s12532-024-00264-w","pdf_url":"https://link.springer.com/content/pdf/10.1007/s12532-024-00264-w.pdf","source":{"id":"https://openalex.org/S173077093","display_name":"Mathematical Programming Computation","issn_l":"1867-2949","issn":["1867-2949","1867-2957"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematical Programming Computation","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1007/s12532-024-00264-w","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s12532-024-00264-w","pdf_url":"https://link.springer.com/content/pdf/10.1007/s12532-024-00264-w.pdf","source":{"id":"https://openalex.org/S173077093","display_name":"Mathematical Programming Computation","issn_l":"1867-2949","issn":["1867-2949","1867-2957"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematical Programming Computation","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W4402307095.pdf"},"referenced_works_count":45,"referenced_works":["https://openalex.org/W1024110","https://openalex.org/W1516536271","https://openalex.org/W1531674983","https://openalex.org/W1993716282","https://openalex.org/W1999613943","https://openalex.org/W2000210554","https://openalex.org/W2009190506","https://openalex.org/W2012806883","https://openalex.org/W2025486357","https://openalex.org/W2026578200","https://openalex.org/W2028783114","https://openalex.org/W2029734006","https://openalex.org/W2049049772","https://openalex.org/W2055993677","https://openalex.org/W2075379600","https://openalex.org/W2085850581","https://openalex.org/W2086867325","https://openalex.org/W2091354775","https://openalex.org/W2093277124","https://openalex.org/W2101504517","https://openalex.org/W2104842300","https://openalex.org/W2115967956","https://openalex.org/W2120575449","https://openalex.org/W2124927563","https://openalex.org/W2128202699","https://openalex.org/W2135682522","https://openalex.org/W2268390549","https://openalex.org/W2301261742","https://openalex.org/W2538115612","https://openalex.org/W2552835512","https://openalex.org/W2584020404","https://openalex.org/W2616230563","https://openalex.org/W2773474135","https://openalex.org/W2951179629","https://openalex.org/W2963419410","https://openalex.org/W2981978625","https://openalex.org/W2990130760","https://openalex.org/W3099246670","https://openalex.org/W3100072452","https://openalex.org/W3100495456","https://openalex.org/W3101439669","https://openalex.org/W3103309976","https://openalex.org/W3104302389","https://openalex.org/W3165707262","https://openalex.org/W4255442211"],"related_works":["https://openalex.org/W2036562274","https://openalex.org/W2269291726","https://openalex.org/W2121045497","https://openalex.org/W2128202699","https://openalex.org/W2239063252","https://openalex.org/W2165349700","https://openalex.org/W2461836650","https://openalex.org/W2386411162","https://openalex.org/W1997197201","https://openalex.org/W2014318473"],"abstract_inverted_index":{"Abstract":[0],"We":[1,31,54],"study":[2],"a":[3,43,72],"primal-dual":[4],"interior":[5],"point":[6],"method":[7,45],"specialized":[8],"to":[9,46,57],"clustered":[10],"low-rank":[11],"semidefinite":[12],"programs":[13,25],"requiring":[14],"high":[15],"precision":[16],"numerics,":[17],"which":[18,69,100],"arise":[19],"from":[20],"certain":[21],"multivariate":[22],"polynomial":[23],"(matrix)":[24],"through":[26,88,103],"sums-of-squares":[27],"characterizations":[28],"and":[29,37,51],"sampling.":[30],"consider":[32],"the":[33,58,64,78,107],"interplay":[34],"of":[35,60,80],"sampling":[36],"symmetry":[38],"reduction":[39],"as":[40,42],"well":[41,93],"greedy":[44],"obtain":[47],"numerically":[48],"good":[49],"bases":[50],"sample":[52],"points.":[53],"apply":[55],"this":[56],"computation":[59,79],"three-point":[61],"bounds":[62,84],"for":[63,68,77,94,106],"kissing":[65,82],"number":[66,83],"problem,":[67],"we":[70,101],"show":[71,102],"significant":[73],"speedup.":[74],"This":[75],"allows":[76],"improved":[81],"in":[85],"dimensions":[86],"11":[87],"23.":[89],"The":[90],"approach":[91],"performs":[92],"problems":[95],"with":[96],"bad":[97],"numerical":[98],"conditioning,":[99],"new":[104],"computations":[105],"binary":[108],"sphere":[109],"packing":[110],"problem.":[111]},"counts_by_year":[{"year":2025,"cited_by_count":4},{"year":2024,"cited_by_count":1}],"updated_date":"2026-05-21T09:19:25.381259","created_date":"2025-10-10T00:00:00"}