{"id":"https://openalex.org/W344589545","doi":"https://doi.org/10.1007/978-3-0348-9297-1_23","title":"On Recent Developments in Linear Programming","display_name":"On Recent Developments in Linear Programming","publication_year":1988,"publication_date":"1988-01-01","ids":{"openalex":"https://openalex.org/W344589545","doi":"https://doi.org/10.1007/978-3-0348-9297-1_23","mag":"344589545"},"language":"en","primary_location":{"id":"doi:10.1007/978-3-0348-9297-1_23","doi":"https://doi.org/10.1007/978-3-0348-9297-1_23","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-3-0348-9297-1_23","pdf_url":null,"source":{"id":"https://openalex.org/S4306462920","display_name":"Birkh\u00e4user Basel eBooks","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"ebook platform"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Trends in Mathematical Optimization","raw_type":"book-chapter"},"volume":{"id":"https://openalex.org/W2499342028","display_name":"Trends in Mathematical Optimization"},"type":"book-chapter","is_traditional":true,"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/A5039879204","display_name":"Uwe T. Zimmermann","orcid":"https://orcid.org/0000-0002-1353-8411","observed_orcids":["https://orcid.org/0000-0002-1353-8411"]},"institutions":[{"id":"https://openalex.org/I94509681","display_name":"Technische Universit\u00e4t Braunschweig","ror":"https://ror.org/010nsgg66","country_code":"DE","type":"education","lineage":["https://openalex.org/I94509681"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Uwe Zimmermann","raw_affiliation_strings":["Abteilung f\u00fcr Mathematische Optimierung, Universit\u00e4t Braunschweig, 3300, Braunschweig, West Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Abteilung f\u00fcr Mathematische Optimierung, Universit\u00e4t Braunschweig, 3300, Braunschweig, West Germany","institution_ids":["https://openalex.org/I94509681"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5039879204"],"corresponding_institution_ids":["https://openalex.org/I94509681"],"apc_list":null,"apc_paid":null,"fwci":1.7,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.77279102,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"353","last_page":"390"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9175000190734863,"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/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9175000190734863,"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/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.0794999971985817,"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/T12709","display_name":"Optimization and Mathematical Programming","score":0.0007999999797903001,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/linear-programming","display_name":"linear programming","score":0.996999979019165},{"id":"https://openalex.org/keywords/simplex-method","display_name":"simplex method","score":0.8830000162124634},{"id":"https://openalex.org/keywords/polynomial-time-algorithms","display_name":"polynomial-time algorithms","score":0.7720000147819519},{"id":"https://openalex.org/keywords/worst-case-complexity","display_name":"worst-case complexity","score":0.7789999842643738},{"id":"https://openalex.org/keywords/average-case-analysis","display_name":"average-case analysis","score":0.8330000042915344}],"concepts":[{"id":"https://openalex.org/C144521790","wikidata":"https://www.wikidata.org/wiki/Q134164","display_name":"Simplex algorithm","level":3,"score":0.9071547985076904},{"id":"https://openalex.org/C41045048","wikidata":"https://www.wikidata.org/wiki/Q202843","display_name":"Linear programming","level":2,"score":0.7911439538002014},{"id":"https://openalex.org/C191157680","wikidata":"https://www.wikidata.org/wiki/Q17085895","display_name":"Revised simplex method","level":4,"score":0.7805981636047363},{"id":"https://openalex.org/C62438384","wikidata":"https://www.wikidata.org/wiki/Q331350","display_name":"Simplex","level":2,"score":0.6806727647781372},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.48957380652427673},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4844098687171936},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.4516699016094208},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.38598135113716125},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3375436067581177},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.13225746154785156},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/978-3-0348-9297-1_23","doi":"https://doi.org/10.1007/978-3-0348-9297-1_23","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-3-0348-9297-1_23","pdf_url":null,"source":{"id":"https://openalex.org/S4306462920","display_name":"Birkh\u00e4user Basel eBooks","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"ebook platform"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Trends in Mathematical Optimization","raw_type":"book-chapter"}],"best_oa_location":null,"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":50,"referenced_works":["https://openalex.org/W15168620","https://openalex.org/W31861061","https://openalex.org/W61120940","https://openalex.org/W1500913691","https://openalex.org/W1516508621","https://openalex.org/W1554963797","https://openalex.org/W1561880747","https://openalex.org/W1571051474","https://openalex.org/W1601677479","https://openalex.org/W1976210548","https://openalex.org/W1976756318","https://openalex.org/W1980845317","https://openalex.org/W1982967176","https://openalex.org/W1987920272","https://openalex.org/W1987953347","https://openalex.org/W1996025842","https://openalex.org/W2001695417","https://openalex.org/W2012329067","https://openalex.org/W2014746566","https://openalex.org/W2017991145","https://openalex.org/W2024448501","https://openalex.org/W2026021734","https://openalex.org/W2029121424","https://openalex.org/W2031629837","https://openalex.org/W2033040247","https://openalex.org/W2034899375","https://openalex.org/W2036021825","https://openalex.org/W2037650903","https://openalex.org/W2059014132","https://openalex.org/W2066014015","https://openalex.org/W2076768004","https://openalex.org/W2079387634","https://openalex.org/W2086920040","https://openalex.org/W2091195410","https://openalex.org/W2091964672","https://openalex.org/W2093000738","https://openalex.org/W2094326251","https://openalex.org/W2097897435","https://openalex.org/W2107501462","https://openalex.org/W2124861949","https://openalex.org/W2155500999","https://openalex.org/W2185161332","https://openalex.org/W2268260714","https://openalex.org/W2326806701","https://openalex.org/W2482182218","https://openalex.org/W2611147814","https://openalex.org/W2798909945","https://openalex.org/W4230397637","https://openalex.org/W4234696559","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W15168620","https://openalex.org/W4388321744","https://openalex.org/W1993541808","https://openalex.org/W2017177415","https://openalex.org/W102721416","https://openalex.org/W7125966413","https://openalex.org/W4302841744","https://openalex.org/W7218039556","https://openalex.org/W4247047926","https://openalex.org/W2259719357"],"abstract_inverted_index":{"Linear":[0,20],"programming":[1],"remains":[2],"a":[3,75,131],"central":[4],"subject":[5],"of":[6,48,70,78,108,124,134,138],"Mathematical":[7],"Programming":[8,21],"although":[9],"already":[10],"in":[11,28,45,60,74],"1947,":[12],"Dantzig":[13],"developed":[14],"the":[15,42,46,55,61,68,79,109,120,125,139,144,158,165,171],"Simplex":[16,56,80,126,140],"method":[17,24,57,127,141],"for":[18,36],"solving":[19,37],"problems.":[22,40],"That":[23],"has":[25],"been":[26,94],"implemented":[27],"quite":[29],"powerful":[30],"codes":[31],"which":[32],"are":[33],"very":[34],"efficient":[35,122],"real":[38],"world":[39],"With":[41],"growing":[43],"interest":[44],"complexity":[47],"algorithms,":[49],"however,":[50],"it":[51],"turned":[52],"out":[53],"that":[54],"is":[58,82,101,112,162],"exponential":[59],"worst":[62,97],"case":[63,98,111,136],"(Klee-Minty":[64],"[1972]).":[65],"Until":[66],"now":[67],"existence":[69],"pivoting":[71],"rules":[72,89],"resulting":[73],"polynomial":[76],"variant":[77],"Method":[81],"an":[83],"open":[84],"question.":[85],"For":[86,130],"most":[87],"known":[88],"conterexamples":[90],"to":[91,103,118,146],"polynomiality":[92],"have":[93],"constructed.":[95],"The":[96,106],"approach":[99],"itself":[100],"due":[102],"much":[104,114,128],"criticizm.":[105],"analysis":[107,137],"average":[110,135],"usually":[113],"harder,":[115],"but":[116],"seems":[117],"explain":[119],"typically":[121],"performance":[123],"better.":[129],"broad":[132],"discussion":[133],"we":[142],"refer":[143],"reader":[145],"Borgwardt":[147],"[1984].":[148],"These":[149],"keywords":[150,166],"were":[151],"added":[152],"by":[153,157],"machine":[154],"and":[155,164],"not":[156],"authors.":[159],"This":[160],"process":[161],"experimental":[163],"may":[167],"be":[168],"updated":[169],"as":[170],"learning":[172],"algorithm":[173],"improves.":[174]},"counts_by_year":[],"updated_date":"2026-11-04T10:54:05.112534","created_date":"2016-06-24T00:00:00"}
