{"id":"https://openalex.org/W4385278298","doi":"https://doi.org/10.3390/a16080356","title":"A State of the Art Review of Systems of Linear Inequalities and Related Observability Problems","display_name":"A State of the Art Review of Systems of Linear Inequalities and Related Observability Problems","publication_year":2023,"publication_date":"2023-07-25","ids":{"openalex":"https://openalex.org/W4385278298","doi":"https://doi.org/10.3390/a16080356"},"language":"en","primary_location":{"id":"doi:10.3390/a16080356","is_oa":true,"landing_page_url":"https://doi.org/10.3390/a16080356","pdf_url":"https://www.mdpi.com/1999-4893/16/8/356/pdf?version=1690354785","source":{"id":"https://openalex.org/S190629608","display_name":"Algorithms","issn_l":"1999-4893","issn":["1999-4893"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Algorithms","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/1999-4893/16/8/356/pdf?version=1690354785","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5102889648","display_name":"Enrique Castillo","orcid":"https://orcid.org/0000-0002-8570-0844"},"institutions":[{"id":"https://openalex.org/I1288451689","display_name":"Real Academia Espa\u00f1ola","ror":"https://ror.org/05t8ffp36","country_code":"ES","type":"education","lineage":["https://openalex.org/I1288451689"]},{"id":"https://openalex.org/I13134134","display_name":"Universidad de Cantabria","ror":"https://ror.org/046ffzj20","country_code":"ES","type":"education","lineage":["https://openalex.org/I13134134"]}],"countries":["ES"],"is_corresponding":true,"raw_author_name":"Enrique Castillo","raw_affiliation_strings":["Department of Applied Mathematics and Computational Sciences, University of Cantabria, Avda. de Los Castros s/n, 39005 Santander, Spain","Spanish Royal Academy of Engineering, Don Pedro 10, 28005 Madrid, Spain","Spanish Royal Academy of Sciences, Valverde 22, 28004 Madrid, Spain"],"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics and Computational Sciences, University of Cantabria, Avda. de Los Castros s/n, 39005 Santander, Spain","institution_ids":["https://openalex.org/I13134134"]},{"raw_affiliation_string":"Spanish Royal Academy of Engineering, Don Pedro 10, 28005 Madrid, Spain","institution_ids":["https://openalex.org/I1288451689"]},{"raw_affiliation_string":"Spanish Royal Academy of Sciences, Valverde 22, 28004 Madrid, Spain","institution_ids":["https://openalex.org/I1288451689"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5102889648"],"corresponding_institution_ids":["https://openalex.org/I1288451689","https://openalex.org/I13134134"],"apc_list":{"value":1400,"currency":"CHF","value_usd":1515},"apc_paid":{"value":1400,"currency":"CHF","value_usd":1515},"fwci":1.2339,"has_fulltext":true,"cited_by_count":3,"citation_normalized_percentile":{"value":0.75282631,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":"16","issue":"8","first_page":"356","last_page":"356"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9983000159263611,"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":0.9983000159263611,"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/T10928","display_name":"Probabilistic and Robust Engineering Design","score":0.9717000126838684,"subfield":{"id":"https://openalex.org/subfields/1804","display_name":"Statistics, Probability and Uncertainty"},"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/T11236","display_name":"Control Systems and Identification","score":0.9674999713897705,"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/observability","display_name":"Observability","score":0.710727334022522},{"id":"https://openalex.org/keywords/linear-inequality","display_name":"Linear inequality","score":0.6747115850448608},{"id":"https://openalex.org/keywords/polytope","display_name":"Polytope","score":0.6209482550621033},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.5339623093605042},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.5079236626625061},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4979746341705322},{"id":"https://openalex.org/keywords/polyhedron","display_name":"Polyhedron","score":0.4866993725299835},{"id":"https://openalex.org/keywords/linear-programming","display_name":"Linear programming","score":0.47816023230552673},{"id":"https://openalex.org/keywords/solution-set","display_name":"Solution set","score":0.4467686116695404},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4403397738933563},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.37959128618240356},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.36304396390914917},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3463938236236572},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.30912962555885315},{"id":"https://openalex.org/keywords/inequality","display_name":"Inequality","score":0.27144908905029297},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.2257629930973053},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.20876652002334595},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.146945983171463},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.11301198601722717}],"concepts":[{"id":"https://openalex.org/C36299963","wikidata":"https://www.wikidata.org/wiki/Q1369844","display_name":"Observability","level":2,"score":0.710727334022522},{"id":"https://openalex.org/C84135550","wikidata":"https://www.wikidata.org/wiki/Q3154022","display_name":"Linear inequality","level":3,"score":0.6747115850448608},{"id":"https://openalex.org/C145691206","wikidata":"https://www.wikidata.org/wiki/Q747980","display_name":"Polytope","level":2,"score":0.6209482550621033},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.5339623093605042},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.5079236626625061},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4979746341705322},{"id":"https://openalex.org/C54829058","wikidata":"https://www.wikidata.org/wiki/Q172937","display_name":"Polyhedron","level":2,"score":0.4866993725299835},{"id":"https://openalex.org/C41045048","wikidata":"https://www.wikidata.org/wiki/Q202843","display_name":"Linear programming","level":2,"score":0.47816023230552673},{"id":"https://openalex.org/C60033838","wikidata":"https://www.wikidata.org/wiki/Q1751685","display_name":"Solution set","level":3,"score":0.4467686116695404},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4403397738933563},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.37959128618240356},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.36304396390914917},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3463938236236572},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.30912962555885315},{"id":"https://openalex.org/C45555294","wikidata":"https://www.wikidata.org/wiki/Q28113351","display_name":"Inequality","level":2,"score":0.27144908905029297},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.2257629930973053},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.20876652002334595},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.146945983171463},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.11301198601722717},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/a16080356","is_oa":true,"landing_page_url":"https://doi.org/10.3390/a16080356","pdf_url":"https://www.mdpi.com/1999-4893/16/8/356/pdf?version=1690354785","source":{"id":"https://openalex.org/S190629608","display_name":"Algorithms","issn_l":"1999-4893","issn":["1999-4893"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Algorithms","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:86701f6d2bd44539843ba6fe03f3914a","is_oa":true,"landing_page_url":"https://doaj.org/article/86701f6d2bd44539843ba6fe03f3914a","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Algorithms, Vol 16, Iss 8, p 356 (2023)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/1999-4893/16/8/356/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/a16080356","pdf_url":null,"source":{"id":"https://openalex.org/S4306400947","display_name":"MDPI (MDPI AG)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210097602","host_organization_name":"Multidisciplinary Digital Publishing Institute (Switzerland)","host_organization_lineage":["https://openalex.org/I4210097602"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Algorithms; Volume 16; Issue 8; Pages: 356","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/a16080356","is_oa":true,"landing_page_url":"https://doi.org/10.3390/a16080356","pdf_url":"https://www.mdpi.com/1999-4893/16/8/356/pdf?version=1690354785","source":{"id":"https://openalex.org/S190629608","display_name":"Algorithms","issn_l":"1999-4893","issn":["1999-4893"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Algorithms","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4385278298.pdf","grobid_xml":"https://content.openalex.org/works/W4385278298.grobid-xml"},"referenced_works_count":32,"referenced_works":["https://openalex.org/W584370323","https://openalex.org/W1943012239","https://openalex.org/W1964803097","https://openalex.org/W1977211467","https://openalex.org/W1979679587","https://openalex.org/W1991287453","https://openalex.org/W2018343880","https://openalex.org/W2020804487","https://openalex.org/W2030334004","https://openalex.org/W2035814233","https://openalex.org/W2040001804","https://openalex.org/W2072648768","https://openalex.org/W2076476551","https://openalex.org/W2079789648","https://openalex.org/W2084324684","https://openalex.org/W2099259622","https://openalex.org/W2102980337","https://openalex.org/W2107383972","https://openalex.org/W2121853705","https://openalex.org/W2152748215","https://openalex.org/W2234624183","https://openalex.org/W2492353954","https://openalex.org/W2493111772","https://openalex.org/W2906482729","https://openalex.org/W4234356172","https://openalex.org/W4298869871","https://openalex.org/W4301491118","https://openalex.org/W4319308362","https://openalex.org/W4362560727","https://openalex.org/W4381461339","https://openalex.org/W4381712570","https://openalex.org/W6723406818"],"related_works":["https://openalex.org/W2038958829","https://openalex.org/W2014648931","https://openalex.org/W2081650204","https://openalex.org/W1979390716","https://openalex.org/W4387908483","https://openalex.org/W1993108008","https://openalex.org/W4281748523","https://openalex.org/W2742362764","https://openalex.org/W1498853542","https://openalex.org/W1566716345"],"abstract_inverted_index":{"This":[0],"work":[1,70],"is":[2,190],"a":[3,46,53,153,173],"short":[4],"review":[5],"of":[6,9,21,23,38,42,45,81,127,137,152,163,187,201,211,216,223,227],"the":[7,10,16,35,43,83,97,104,113,125,164,185,199,221],"state":[8],"art":[11],"aiming":[12],"to":[13,15,60,158,198,213],"contribute":[14],"use,":[17],"disclosure,":[18],"and":[19,30,52,55,75,78,87,93,112,122,132,145,167,192],"propagation":[20],"systems":[22,80,226],"linear":[24,47,179],"inequalities":[25],"in":[26,62,107,142],"real":[27,108],"life,":[28],"teaching,":[29],"research.":[31],"It":[32],"shows":[33],"that":[34,56,204],"algebraic":[36],"structure":[37],"their":[39,63,88,117],"solutions":[40,131,151,160,189,194],"consists":[41],"sum":[44],"subspace,":[48],"an":[49],"acute":[50],"cone,":[51],"polytope,":[54],"adequate":[57],"software":[58],"exists":[59],"obtain,":[61],"simplest":[64],"forms,":[65,119],"these":[66,225],"three":[67],"components.":[68],"The":[69,110,178],"describes,":[71],"based":[72],"on":[73],"orthogonality":[74],"polarity,":[76],"homogeneous":[77],"complete":[79],"inequalities,":[82],"associated":[84],"compatibility":[85,111],"problems,":[86,103,115],"relations":[89],"with":[90,129,139],"convex":[91],"polyhedra":[92],"polytopes,":[94],"which":[95],"are":[96,120,195,218],"only":[98,206],"possible":[99],"solution":[100],"for":[101,176],"bounded":[102],"most":[105],"common":[106,174],"practice.":[109],"observability":[114],"including":[116],"symbolic":[118],"analyzed":[121],"solved,":[123],"identifying":[124],"subsets":[126],"unknowns":[128],"unique":[130],"those":[133],"unbounded,":[134],"important":[135],"items":[136],"information":[138],"practical":[140],"relevance":[141],"artificial":[143],"intelligence":[144],"automatic":[146],"learning.":[147],"Having":[148],"infinitely":[149],"many":[150],"given":[154],"problem":[155,181],"allows":[156],"us":[157],"find":[159],"when":[161,184],"some":[162],"assumptions":[165],"fail":[166],"unexpected":[168],"constraints":[169],"come":[170],"into":[171],"play,":[172],"situation":[175],"engineers.":[177],"programming":[180],"becomes":[182],"trivial":[183],"set":[186],"all":[188,193],"available":[191],"obtained,":[196],"contrary":[197],"case":[200],"standard":[202],"programs":[203],"provide":[205],"one":[207],"solution.":[208],"Several":[209],"examples":[210],"applications":[212],"several":[214],"areas":[215],"knowledge":[217],"presented,":[219],"illustrating":[220],"advantages":[222],"solving":[224],"inequalities.":[228]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":1}],"updated_date":"2026-02-28T09:26:25.869077","created_date":"2025-10-10T00:00:00"}