{"id":"https://openalex.org/W2578091951","doi":"https://doi.org/10.1080/10556788.2016.1270279","title":"The solution of euclidean norm trust region SQP subproblems via second-order cone programs: an overview and elementary introduction","display_name":"The solution of euclidean norm trust region SQP subproblems via second-order cone programs: an overview and elementary introduction","publication_year":2017,"publication_date":"2017-01-18","ids":{"openalex":"https://openalex.org/W2578091951","doi":"https://doi.org/10.1080/10556788.2016.1270279","mag":"2578091951"},"language":"en","primary_location":{"id":"doi:10.1080/10556788.2016.1270279","is_oa":false,"landing_page_url":"https://doi.org/10.1080/10556788.2016.1270279","pdf_url":null,"source":{"id":"https://openalex.org/S103047102","display_name":"Optimization methods & software","issn_l":"1026-7670","issn":["1026-7670","1029-4937","1055-6788"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Optimization Methods and Software","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/A5015422470","display_name":"Florian Jarre","orcid":"https://orcid.org/0000-0003-3458-123X"},"institutions":[{"id":"https://openalex.org/I44260953","display_name":"Heinrich Heine University D\u00fcsseldorf","ror":"https://ror.org/024z2rq82","country_code":"DE","type":"education","lineage":["https://openalex.org/I44260953"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Florian Jarre","raw_affiliation_strings":["Mathematisches Institut, Universitaet Duesseldorf, Universitaetsstr. 1, 40225 Duesseldorf, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Mathematisches Institut, Universitaet Duesseldorf, Universitaetsstr. 1, 40225 Duesseldorf, Germany","institution_ids":["https://openalex.org/I44260953"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5032927599","display_name":"Felix Lieder","orcid":"https://orcid.org/0000-0002-5276-2010"},"institutions":[{"id":"https://openalex.org/I44260953","display_name":"Heinrich Heine University D\u00fcsseldorf","ror":"https://ror.org/024z2rq82","country_code":"DE","type":"education","lineage":["https://openalex.org/I44260953"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Felix Lieder","raw_affiliation_strings":["Department of Mathematics, Heinrich-Heine-Universitat Dusseldorf, Universitaetsstr. 1, 40225 Dusseldorf, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Heinrich-Heine-Universitat Dusseldorf, Universitaetsstr. 1, 40225 Dusseldorf, Germany","institution_ids":["https://openalex.org/I44260953"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5015422470"],"corresponding_institution_ids":["https://openalex.org/I44260953"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.0175482,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"33","issue":"1","first_page":"70","last_page":"91"},"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/T10791","display_name":"Advanced Control Systems Optimization","score":0.9944999814033508,"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/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9908999800682068,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/sequential-quadratic-programming","display_name":"Sequential quadratic programming","score":0.7522615194320679},{"id":"https://openalex.org/keywords/interior-point-method","display_name":"Interior point method","score":0.7430993318557739},{"id":"https://openalex.org/keywords/trust-region","display_name":"Trust region","score":0.7289528250694275},{"id":"https://openalex.org/keywords/euclidean-geometry","display_name":"Euclidean geometry","score":0.6607613563537598},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5926626920700073},{"id":"https://openalex.org/keywords/second-order-cone-programming","display_name":"Second-order cone programming","score":0.5461857914924622},{"id":"https://openalex.org/keywords/norm","display_name":"Norm (philosophy)","score":0.5220561027526855},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5202266573905945},{"id":"https://openalex.org/keywords/quadratic-equation","display_name":"Quadratic equation","score":0.44236335158348083},{"id":"https://openalex.org/keywords/euclidean-distance","display_name":"Euclidean distance","score":0.4388246536254883},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.41293537616729736},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.35393571853637695},{"id":"https://openalex.org/keywords/quadratic-programming","display_name":"Quadratic programming","score":0.3495175838470459},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.33098289370536804},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.24620473384857178},{"id":"https://openalex.org/keywords/convex-optimization","display_name":"Convex optimization","score":0.21878784894943237},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.18865731358528137},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.07769915461540222}],"concepts":[{"id":"https://openalex.org/C198927703","wikidata":"https://www.wikidata.org/wiki/Q4373881","display_name":"Sequential quadratic programming","level":3,"score":0.7522615194320679},{"id":"https://openalex.org/C155253501","wikidata":"https://www.wikidata.org/wiki/Q461992","display_name":"Interior point method","level":2,"score":0.7430993318557739},{"id":"https://openalex.org/C89109886","wikidata":"https://www.wikidata.org/wiki/Q1535924","display_name":"Trust region","level":3,"score":0.7289528250694275},{"id":"https://openalex.org/C129782007","wikidata":"https://www.wikidata.org/wiki/Q162886","display_name":"Euclidean geometry","level":2,"score":0.6607613563537598},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5926626920700073},{"id":"https://openalex.org/C111397411","wikidata":"https://www.wikidata.org/wiki/Q7442977","display_name":"Second-order cone programming","level":4,"score":0.5461857914924622},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.5220561027526855},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5202266573905945},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.44236335158348083},{"id":"https://openalex.org/C120174047","wikidata":"https://www.wikidata.org/wiki/Q847073","display_name":"Euclidean distance","level":2,"score":0.4388246536254883},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.41293537616729736},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.35393571853637695},{"id":"https://openalex.org/C81845259","wikidata":"https://www.wikidata.org/wiki/Q290117","display_name":"Quadratic programming","level":2,"score":0.3495175838470459},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.33098289370536804},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.24620473384857178},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.21878784894943237},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.18865731358528137},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.07769915461540222},{"id":"https://openalex.org/C38652104","wikidata":"https://www.wikidata.org/wiki/Q3510521","display_name":"Computer security","level":1,"score":0.0},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0},{"id":"https://openalex.org/C178635117","wikidata":"https://www.wikidata.org/wiki/Q747499","display_name":"RADIUS","level":2,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1080/10556788.2016.1270279","is_oa":false,"landing_page_url":"https://doi.org/10.1080/10556788.2016.1270279","pdf_url":null,"source":{"id":"https://openalex.org/S103047102","display_name":"Optimization methods & software","issn_l":"1026-7670","issn":["1026-7670","1029-4937","1055-6788"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Optimization Methods and Software","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":45,"referenced_works":["https://openalex.org/W2572016","https://openalex.org/W10800830","https://openalex.org/W82689443","https://openalex.org/W147998453","https://openalex.org/W170686111","https://openalex.org/W1518039036","https://openalex.org/W1568307856","https://openalex.org/W1941836914","https://openalex.org/W1967073510","https://openalex.org/W1968745099","https://openalex.org/W1970050176","https://openalex.org/W1981027849","https://openalex.org/W1984610741","https://openalex.org/W1989033306","https://openalex.org/W1996045511","https://openalex.org/W1999356624","https://openalex.org/W2004747456","https://openalex.org/W2006980285","https://openalex.org/W2009923109","https://openalex.org/W2009941369","https://openalex.org/W2010364290","https://openalex.org/W2011039300","https://openalex.org/W2012110988","https://openalex.org/W2025251058","https://openalex.org/W2033758151","https://openalex.org/W2048799772","https://openalex.org/W2066459185","https://openalex.org/W2075184363","https://openalex.org/W2077274614","https://openalex.org/W2080108722","https://openalex.org/W2085595139","https://openalex.org/W2086867325","https://openalex.org/W2090180723","https://openalex.org/W2092377825","https://openalex.org/W2105235982","https://openalex.org/W2110540077","https://openalex.org/W2117065890","https://openalex.org/W2121274191","https://openalex.org/W2129516068","https://openalex.org/W2156005216","https://openalex.org/W2252194181","https://openalex.org/W2572594781","https://openalex.org/W4250589301","https://openalex.org/W4252814261","https://openalex.org/W6959836603"],"related_works":["https://openalex.org/W574348691","https://openalex.org/W2388495914","https://openalex.org/W2066134689","https://openalex.org/W4389749172","https://openalex.org/W2069426496","https://openalex.org/W2382819838","https://openalex.org/W2402755997","https://openalex.org/W2021667348","https://openalex.org/W2059043079","https://openalex.org/W2070265719"],"abstract_inverted_index":{"It":[0],"is":[1,51,66,112,145,159],"well":[2,60],"known":[3],"that":[4,158],"convex":[5],"sequential":[6],"quadratic":[7],"programming":[8],"(SQP)":[9],"subproblems":[10,58],"with":[11,139],"an":[12,49,115],"Euclidean":[13,30],"norm":[14],"trust":[15],"region":[16],"constraint":[17],"can":[18,96],"be":[19,97],"reduced":[20],"to":[21,34,56,62,81,136],"second-order":[22],"cone":[23],"programs":[24,86],"for":[25,71,84,105,108,117,120,161],"which":[26],"the":[27,45,54,72,90,93,101,134,149],"theory":[28],"of":[29,44,47,89,92,151],"Jordan":[31,127],"algebras":[32,128],"leads":[33],"efficient":[35],"interior-point":[36,82,106],"algorithms.":[37],"Here,":[38],"a":[39,155],"brief":[40],"and":[41,53,78,119,148],"self-contained":[42],"outline":[43],"principles":[46],"such":[48],"implementation":[50,73,144],"given":[52],"application":[55],"SQP":[57,94,162],"as":[59,61,104,114],"cubic":[63],"regularization":[64],"problems":[65],"discussed.":[67],"All":[68],"identities":[69],"relevant":[70],"are":[74,79],"derived":[75],"from":[76],"scratch":[77],"compared":[80],"methods":[83,107],"linear":[85],"(LPs).":[87],"Sparsity":[88],"data":[91],"subproblem":[95],"maintained":[98],"essentially":[99],"in":[100],"same":[102],"way":[103],"LPs.":[109],"The":[110],"presentation":[111],"intended":[113],"introduction":[116],"students":[118],"colleagues":[121],"who":[122],"may":[123],"have":[124],"heard":[125],"about":[126],"but":[129],"did":[130],"not":[131],"yet":[132],"find":[133],"time":[135],"get":[137],"involved":[138],"them.":[140],"A":[141],"simple":[142],"Matlab":[143],"made":[146],"available":[147],"discussion":[150],"implementational":[152],"aspects":[153],"addresses":[154],"scaling":[156],"property":[157],"critical":[160],"subproblems.":[163]},"counts_by_year":[{"year":2022,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}