{"id":"https://openalex.org/W3092336956","doi":"https://doi.org/10.1007/s00186-020-00726-6","title":"Interplay of non-convex quadratically constrained problems with adjustable robust optimization","display_name":"Interplay of non-convex quadratically constrained problems with adjustable robust optimization","publication_year":2020,"publication_date":"2020-10-06","ids":{"openalex":"https://openalex.org/W3092336956","doi":"https://doi.org/10.1007/s00186-020-00726-6","mag":"3092336956"},"language":"en","primary_location":{"id":"doi:10.1007/s00186-020-00726-6","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00186-020-00726-6","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00186-020-00726-6.pdf","source":{"id":"https://openalex.org/S126160977","display_name":"Mathematical Methods of Operations Research","issn_l":"1432-2994","issn":["1432-2994","1432-5217"],"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 Methods of Operations Research","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/s00186-020-00726-6.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5023776719","display_name":"Immanuel M. Bomze","orcid":"https://orcid.org/0000-0002-6288-9226"},"institutions":[{"id":"https://openalex.org/I129774422","display_name":"University of Vienna","ror":"https://ror.org/03prydq77","country_code":"AT","type":"education","lineage":["https://openalex.org/I129774422"]}],"countries":["AT"],"is_corresponding":false,"raw_author_name":"Immanuel Bomze","raw_affiliation_strings":["ISOR/VCOR/VGSCO and ds:univie, University of Vienna, Vienna, Austria"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"ISOR/VCOR/VGSCO and ds:univie, University of Vienna, Vienna, Austria","institution_ids":["https://openalex.org/I129774422"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5055915468","display_name":"Markus Gabl","orcid":"https://orcid.org/0000-0002-9598-0106"},"institutions":[{"id":"https://openalex.org/I129774422","display_name":"University of Vienna","ror":"https://ror.org/03prydq77","country_code":"AT","type":"education","lineage":["https://openalex.org/I129774422"]}],"countries":["AT"],"is_corresponding":true,"raw_author_name":"Markus Gabl","raw_affiliation_strings":["ISOR/VCOR/VGSCO and ds:univie, University of Vienna, Vienna, Austria"],"raw_orcid":"https://orcid.org/0000-0002-9598-0106","affiliations":[{"raw_affiliation_string":"ISOR/VCOR/VGSCO and ds:univie, University of Vienna, Vienna, Austria","institution_ids":["https://openalex.org/I129774422"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5055915468"],"corresponding_institution_ids":["https://openalex.org/I129774422"],"apc_list":{"value":2290,"currency":"EUR","value_usd":2890},"apc_paid":{"value":2290,"currency":"EUR","value_usd":2890},"fwci":0.7286,"has_fulltext":true,"cited_by_count":9,"citation_normalized_percentile":{"value":0.77531308,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"93","issue":"1","first_page":"115","last_page":"151"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10545","display_name":"Optimization and Variational Analysis","score":0.9980000257492065,"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"}},"topics":[{"id":"https://openalex.org/T10545","display_name":"Optimization and Variational Analysis","score":0.9980000257492065,"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/T11413","display_name":"Risk and Portfolio Optimization","score":0.9977999925613403,"subfield":{"id":"https://openalex.org/subfields/1803","display_name":"Management Science and Operations Research"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9975000023841858,"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/quadratic-growth","display_name":"Quadratic growth","score":0.7885167002677917},{"id":"https://openalex.org/keywords/conic-optimization","display_name":"Conic optimization","score":0.7072230577468872},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.6285220980644226},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6248109936714172},{"id":"https://openalex.org/keywords/convex-optimization","display_name":"Convex optimization","score":0.5368798971176147},{"id":"https://openalex.org/keywords/quadratically-constrained-quadratic-program","display_name":"Quadratically constrained quadratic program","score":0.5317042469978333},{"id":"https://openalex.org/keywords/robust-optimization","display_name":"Robust optimization","score":0.5309455394744873},{"id":"https://openalex.org/keywords/optimization-problem","display_name":"Optimization problem","score":0.52866530418396},{"id":"https://openalex.org/keywords/quadratic-equation","display_name":"Quadratic equation","score":0.5101178288459778},{"id":"https://openalex.org/keywords/second-order-cone-programming","display_name":"Second-order cone programming","score":0.44287392497062683},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.3947816491127014},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.372470885515213},{"id":"https://openalex.org/keywords/quadratic-programming","display_name":"Quadratic programming","score":0.35599637031555176},{"id":"https://openalex.org/keywords/convex-analysis","display_name":"Convex analysis","score":0.30586275458335876},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.2067750096321106}],"concepts":[{"id":"https://openalex.org/C195956108","wikidata":"https://www.wikidata.org/wiki/Q7268362","display_name":"Quadratic growth","level":2,"score":0.7885167002677917},{"id":"https://openalex.org/C79187972","wikidata":"https://www.wikidata.org/wiki/Q2654791","display_name":"Conic optimization","level":5,"score":0.7072230577468872},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.6285220980644226},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6248109936714172},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.5368798971176147},{"id":"https://openalex.org/C65148998","wikidata":"https://www.wikidata.org/wiki/Q7268373","display_name":"Quadratically constrained quadratic program","level":3,"score":0.5317042469978333},{"id":"https://openalex.org/C193254401","wikidata":"https://www.wikidata.org/wiki/Q2160088","display_name":"Robust optimization","level":2,"score":0.5309455394744873},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.52866530418396},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.5101178288459778},{"id":"https://openalex.org/C111397411","wikidata":"https://www.wikidata.org/wiki/Q7442977","display_name":"Second-order cone programming","level":4,"score":0.44287392497062683},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.3947816491127014},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.372470885515213},{"id":"https://openalex.org/C81845259","wikidata":"https://www.wikidata.org/wiki/Q290117","display_name":"Quadratic programming","level":2,"score":0.35599637031555176},{"id":"https://openalex.org/C12108790","wikidata":"https://www.wikidata.org/wiki/Q2234833","display_name":"Convex analysis","level":4,"score":0.30586275458335876},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.2067750096321106},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/s00186-020-00726-6","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00186-020-00726-6","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00186-020-00726-6.pdf","source":{"id":"https://openalex.org/S126160977","display_name":"Mathematical Methods of Operations Research","issn_l":"1432-2994","issn":["1432-2994","1432-5217"],"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 Methods of Operations Research","raw_type":"journal-article"},{"id":"pmh:oai:RePEc:spr:mathme:v:93:y:2021:i:1:d:10.1007_s00186-020-00726-6","is_oa":false,"landing_page_url":"http://link.springer.com/10.1007/s00186-020-00726-6","pdf_url":null,"source":{"id":"https://openalex.org/S4306401271","display_name":"RePEc: Research Papers in Economics","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I77793887","host_organization_name":"Federal Reserve Bank of St. Louis","host_organization_lineage":["https://openalex.org/I77793887"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"doi:10.1007/s00186-020-00726-6","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00186-020-00726-6","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00186-020-00726-6.pdf","source":{"id":"https://openalex.org/S126160977","display_name":"Mathematical Methods of Operations Research","issn_l":"1432-2994","issn":["1432-2994","1432-5217"],"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 Methods of Operations Research","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G6389310286","display_name":"Vienna Graduate School on Computational Optimization","funder_award_id":"W 1260","funder_id":"https://openalex.org/F4320321181","funder_display_name":"Austrian Science Fund"},{"id":"https://openalex.org/G665012019","display_name":null,"funder_award_id":"W 1260-N35","funder_id":"https://openalex.org/F4320321181","funder_display_name":"Austrian Science Fund"}],"funders":[{"id":"https://openalex.org/F4320321181","display_name":"Austrian Science Fund","ror":"https://ror.org/013tf3c58"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3092336956.pdf","grobid_xml":"https://content.openalex.org/works/W3092336956.grobid-xml"},"referenced_works_count":36,"referenced_works":["https://openalex.org/W1518832340","https://openalex.org/W1522995151","https://openalex.org/W1549791526","https://openalex.org/W1969807530","https://openalex.org/W1972746552","https://openalex.org/W1978500232","https://openalex.org/W1986865581","https://openalex.org/W2004392729","https://openalex.org/W2005037112","https://openalex.org/W2005102197","https://openalex.org/W2025776604","https://openalex.org/W2026856626","https://openalex.org/W2031279008","https://openalex.org/W2042816232","https://openalex.org/W2078600458","https://openalex.org/W2089914558","https://openalex.org/W2094753536","https://openalex.org/W2100541427","https://openalex.org/W2110540077","https://openalex.org/W2118807841","https://openalex.org/W2124038748","https://openalex.org/W2124487034","https://openalex.org/W2131712693","https://openalex.org/W2140214428","https://openalex.org/W2140246586","https://openalex.org/W2158226611","https://openalex.org/W2611911673","https://openalex.org/W2891879843","https://openalex.org/W2907897545","https://openalex.org/W2962689628","https://openalex.org/W2973191611","https://openalex.org/W3034208633","https://openalex.org/W3143187486","https://openalex.org/W4248179398","https://openalex.org/W4251616545","https://openalex.org/W4256141204"],"related_works":["https://openalex.org/W2004392729","https://openalex.org/W4298879965","https://openalex.org/W2951903936","https://openalex.org/W2233303476","https://openalex.org/W2492346510","https://openalex.org/W2169350232","https://openalex.org/W2566013347","https://openalex.org/W3035921962","https://openalex.org/W4297407962","https://openalex.org/W2108515966"],"abstract_inverted_index":{"Abstract":[0],"In":[1],"this":[2,60],"paper":[3],"we":[4,17,79,128],"explore":[5],"convex":[6],"reformulation":[7,82,111,133],"strategies":[8,134],"for":[9,47,63,88,121],"non-convex":[10],"quadratically":[11],"constrained":[12],"optimization":[13,38,90,98,125],"problems":[14,91],"(QCQPs).":[15],"First":[16],"investigate":[18,80,129],"such":[19],"reformulations":[20],"using":[21],"Pataki\u2019s":[22],"rank":[23],"theorem":[24],"iteratively.":[25],"We":[26,100],"show":[27,101],"that":[28],"the":[29,48,58,67,70,75,130],"result":[30],"can":[31,108],"be":[32,51],"used":[33],"in":[34,40,85,115,135],"conjunction":[35],"with":[36],"conic":[37],"duality":[39],"order":[41,116,136],"to":[42,50,117,137],"obtain":[43],"a":[44,81,104],"geometric":[45],"condition":[46],"S-procedure":[49],"exact.":[52],"Based":[53],"upon":[54,147],"known":[55],"results":[56,112],"on":[57,95],"S-procedure,":[59],"approach":[61],"allows":[62],"some":[64],"insight":[65],"into":[66],"geometry":[68],"of":[69,74,113,132,140],"joint":[71],"numerical":[72,149],"range":[73],"quadratic":[76,124],"forms.":[77],"Then":[78],"strategy":[83],"introduced":[84],"recent":[86],"literature":[87],"bilinear":[89],"which":[92],"is":[93],"based":[94,146],"adjustable":[96],"robust":[97],"theory.":[99],"that,":[102],"via":[103],"similar":[105],"strategy,":[106],"one":[107],"leverage":[109],"exact":[110],"QCQPs":[114],"derive":[118,138],"lower":[119],"bounds":[120],"more":[122],"complicated":[123],"problems.":[126],"Finally,":[127],"use":[131],"characterizations":[139],"set-copositive":[141],"matrix":[142],"cones.":[143],"Empirical":[144],"evidence":[145],"first":[148],"experiments":[150],"shows":[151],"encouraging":[152],"results.":[153]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":2}],"updated_date":"2026-06-22T08:00:12.763002","created_date":"2025-10-10T00:00:00"}
