{"id":"https://openalex.org/W2093642032","doi":"https://doi.org/10.1007/bf02023104","title":"On degeneracy in linear programming and related problems","display_name":"On degeneracy in linear programming and related problems","publication_year":1993,"publication_date":"1993-09-01","ids":{"openalex":"https://openalex.org/W2093642032","doi":"https://doi.org/10.1007/bf02023104","mag":"2093642032"},"language":"en","primary_location":{"id":"doi:10.1007/bf02023104","is_oa":false,"landing_page_url":"https://doi.org/10.1007/bf02023104","pdf_url":null,"source":{"id":"https://openalex.org/S57667410","display_name":"Annals of Operations Research","issn_l":"0254-5330","issn":["0254-5330","1572-9338"],"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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Annals of Operations Research","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/A5108541341","display_name":"Karen George","orcid":null},"institutions":[{"id":"https://openalex.org/I188329596","display_name":"University of Canberra","ror":"https://ror.org/04s1nv328","country_code":"AU","type":"education","lineage":["https://openalex.org/I188329596"]}],"countries":["AU"],"is_corresponding":false,"raw_author_name":"Karen George","raw_affiliation_strings":["School of Information Sciences, University of Canberra, Canberra, Australia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Information Sciences, University of Canberra, Canberra, Australia","institution_ids":["https://openalex.org/I188329596"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5103558831","display_name":"M. R. Osborne","orcid":null},"institutions":[{"id":"https://openalex.org/I118347636","display_name":"Australian National University","ror":"https://ror.org/019wvm592","country_code":"AU","type":"education","lineage":["https://openalex.org/I118347636"]},{"id":"https://openalex.org/I2802631561","display_name":"Australian Mathematical Sciences Institute","ror":"https://ror.org/00yn60108","country_code":"AU","type":"other","lineage":["https://openalex.org/I2802631561"]}],"countries":["AU"],"is_corresponding":false,"raw_author_name":"M. R. Osborne","raw_affiliation_strings":["Mathematical Sciences School, Australian National University, Australia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Mathematical Sciences School, Australian National University, Australia","institution_ids":["https://openalex.org/I118347636","https://openalex.org/I2802631561"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":3090,"currency":"USD","value_usd":3090},"apc_paid":null,"fwci":0.4416,"has_fulltext":false,"cited_by_count":7,"citation_normalized_percentile":{"value":0.66072393,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":95},"biblio":{"volume":"46-47","issue":"2","first_page":"343","last_page":"359"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9994000196456909,"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":0.9994000196456909,"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/T10545","display_name":"Optimization and Variational Analysis","score":0.9991000294685364,"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/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9926999807357788,"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/degeneracy","display_name":"Degeneracy (biology)","score":0.9383071064949036},{"id":"https://openalex.org/keywords/degenerate-energy-levels","display_name":"Degenerate energy levels","score":0.7479422092437744},{"id":"https://openalex.org/keywords/gradient-descent","display_name":"Gradient descent","score":0.6757667064666748},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5706065893173218},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5352761149406433},{"id":"https://openalex.org/keywords/minification","display_name":"Minification","score":0.528176486492157},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4834485948085785},{"id":"https://openalex.org/keywords/proximal-gradient-methods","display_name":"Proximal Gradient Methods","score":0.4629085958003998},{"id":"https://openalex.org/keywords/linear-programming","display_name":"Linear programming","score":0.449435830116272},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.44527512788772583},{"id":"https://openalex.org/keywords/gradient-method","display_name":"Gradient method","score":0.4451029300689697},{"id":"https://openalex.org/keywords/extension","display_name":"Extension (predicate logic)","score":0.428364634513855},{"id":"https://openalex.org/keywords/convex-function","display_name":"Convex function","score":0.42763736844062805},{"id":"https://openalex.org/keywords/resolution","display_name":"Resolution (logic)","score":0.41959476470947266},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.37374165654182434},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3578642010688782},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3080436587333679},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.08001893758773804},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.07864728569984436},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.07328566908836365}],"concepts":[{"id":"https://openalex.org/C2777727622","wikidata":"https://www.wikidata.org/wiki/Q5251772","display_name":"Degeneracy (biology)","level":2,"score":0.9383071064949036},{"id":"https://openalex.org/C72319582","wikidata":"https://www.wikidata.org/wiki/Q584304","display_name":"Degenerate energy levels","level":2,"score":0.7479422092437744},{"id":"https://openalex.org/C153258448","wikidata":"https://www.wikidata.org/wiki/Q1199743","display_name":"Gradient descent","level":3,"score":0.6757667064666748},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5706065893173218},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5352761149406433},{"id":"https://openalex.org/C147764199","wikidata":"https://www.wikidata.org/wiki/Q6865248","display_name":"Minification","level":2,"score":0.528176486492157},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4834485948085785},{"id":"https://openalex.org/C10494615","wikidata":"https://www.wikidata.org/wiki/Q17086765","display_name":"Proximal Gradient Methods","level":4,"score":0.4629085958003998},{"id":"https://openalex.org/C41045048","wikidata":"https://www.wikidata.org/wiki/Q202843","display_name":"Linear programming","level":2,"score":0.449435830116272},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.44527512788772583},{"id":"https://openalex.org/C115680565","wikidata":"https://www.wikidata.org/wiki/Q5977448","display_name":"Gradient method","level":2,"score":0.4451029300689697},{"id":"https://openalex.org/C2778029271","wikidata":"https://www.wikidata.org/wiki/Q5421931","display_name":"Extension (predicate logic)","level":2,"score":0.428364634513855},{"id":"https://openalex.org/C145446738","wikidata":"https://www.wikidata.org/wiki/Q319913","display_name":"Convex function","level":3,"score":0.42763736844062805},{"id":"https://openalex.org/C138268822","wikidata":"https://www.wikidata.org/wiki/Q1051925","display_name":"Resolution (logic)","level":2,"score":0.41959476470947266},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.37374165654182434},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3578642010688782},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3080436587333679},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.08001893758773804},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.07864728569984436},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.07328566908836365},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"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/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0},{"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/C60644358","wikidata":"https://www.wikidata.org/wiki/Q128570","display_name":"Bioinformatics","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/bf02023104","is_oa":false,"landing_page_url":"https://doi.org/10.1007/bf02023104","pdf_url":null,"source":{"id":"https://openalex.org/S57667410","display_name":"Annals of Operations Research","issn_l":"0254-5330","issn":["0254-5330","1572-9338"],"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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Annals of Operations Research","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":13,"referenced_works":["https://openalex.org/W60923334","https://openalex.org/W1977187942","https://openalex.org/W1977310057","https://openalex.org/W1997184590","https://openalex.org/W1997958347","https://openalex.org/W2020799833","https://openalex.org/W2044085087","https://openalex.org/W2053732480","https://openalex.org/W2056550768","https://openalex.org/W2083918790","https://openalex.org/W2088128439","https://openalex.org/W2092068641","https://openalex.org/W2335190428"],"related_works":["https://openalex.org/W2811217697","https://openalex.org/W4385644471","https://openalex.org/W4320495396","https://openalex.org/W4295266778","https://openalex.org/W2564172750","https://openalex.org/W2041341337","https://openalex.org/W2037966176","https://openalex.org/W2075334256","https://openalex.org/W2372778757","https://openalex.org/W2026452100"],"abstract_inverted_index":null,"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2026-08-21T09:56:20.448147","created_date":"2025-10-10T00:00:00"}
