{"id":"https://openalex.org/W2034712404","doi":"https://doi.org/10.1137/s1052623494275586","title":"Algorithms for the Generalized Linear Complementarity Problem with a Vertical Block<i>Z</i>-Matrix","display_name":"Algorithms for the Generalized Linear Complementarity Problem with a Vertical Block<i>Z</i>-Matrix","publication_year":1996,"publication_date":"1996-11-01","ids":{"openalex":"https://openalex.org/W2034712404","doi":"https://doi.org/10.1137/s1052623494275586","mag":"2034712404"},"language":"en","primary_location":{"id":"doi:10.1137/s1052623494275586","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s1052623494275586","pdf_url":null,"source":{"id":"https://openalex.org/S928796702","display_name":"SIAM Journal on Optimization","issn_l":"1052-6234","issn":["1052-6234","1095-7189"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Optimization","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/A5109485460","display_name":"S. R. Mohan","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"S. R. Mohan","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5007628003","display_name":"Sarmistha Neogy","orcid":"https://orcid.org/0000-0003-1497-671X"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"S. K. Neogy","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.5168,"has_fulltext":false,"cited_by_count":27,"citation_normalized_percentile":{"value":0.6542199,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"6","issue":"4","first_page":"994","last_page":"1006"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9958999752998352,"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/T10792","display_name":"Matrix Theory and Algorithms","score":0.9958999752998352,"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":0.9907000064849854,"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/T11797","display_name":"graph theory and CDMA systems","score":0.9761000275611877,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic 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/linear-complementarity-problem","display_name":"Linear complementarity problem","score":0.8560437560081482},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8337053060531616},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.6122655272483826},{"id":"https://openalex.org/keywords/simplex-algorithm","display_name":"Simplex algorithm","score":0.5926120281219482},{"id":"https://openalex.org/keywords/block","display_name":"Block (permutation group theory)","score":0.5862887501716614},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.576387345790863},{"id":"https://openalex.org/keywords/complementarity-theory","display_name":"Complementarity theory","score":0.5378908514976501},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.4944148063659668},{"id":"https://openalex.org/keywords/block-matrix","display_name":"Block matrix","score":0.4928886890411377},{"id":"https://openalex.org/keywords/linear-programming","display_name":"Linear programming","score":0.37858495116233826},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.0702851414680481}],"concepts":[{"id":"https://openalex.org/C34320192","wikidata":"https://www.wikidata.org/wiki/Q783105","display_name":"Linear complementarity problem","level":3,"score":0.8560437560081482},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8337053060531616},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.6122655272483826},{"id":"https://openalex.org/C144521790","wikidata":"https://www.wikidata.org/wiki/Q134164","display_name":"Simplex algorithm","level":3,"score":0.5926120281219482},{"id":"https://openalex.org/C2777210771","wikidata":"https://www.wikidata.org/wiki/Q4927124","display_name":"Block (permutation group theory)","level":2,"score":0.5862887501716614},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.576387345790863},{"id":"https://openalex.org/C85404239","wikidata":"https://www.wikidata.org/wiki/Q5156417","display_name":"Complementarity theory","level":3,"score":0.5378908514976501},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4944148063659668},{"id":"https://openalex.org/C85817219","wikidata":"https://www.wikidata.org/wiki/Q884772","display_name":"Block matrix","level":3,"score":0.4928886890411377},{"id":"https://openalex.org/C41045048","wikidata":"https://www.wikidata.org/wiki/Q202843","display_name":"Linear programming","level":2,"score":0.37858495116233826},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.0702851414680481},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/s1052623494275586","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s1052623494275586","pdf_url":null,"source":{"id":"https://openalex.org/S928796702","display_name":"SIAM Journal on Optimization","issn_l":"1052-6234","issn":["1052-6234","1095-7189"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Optimization","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320307769","display_name":"Astellas Pharma US","ror":"https://ror.org/05pw69n24"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":15,"referenced_works":["https://openalex.org/W584634945","https://openalex.org/W1969189939","https://openalex.org/W1990321007","https://openalex.org/W2004250389","https://openalex.org/W2005338952","https://openalex.org/W2005347459","https://openalex.org/W2013321893","https://openalex.org/W2027866950","https://openalex.org/W2030459733","https://openalex.org/W2035164082","https://openalex.org/W2125651385","https://openalex.org/W2127677373","https://openalex.org/W2143370902","https://openalex.org/W2321923742","https://openalex.org/W2948315098"],"related_works":["https://openalex.org/W2133667137","https://openalex.org/W2380756614","https://openalex.org/W2052366866","https://openalex.org/W2371762379","https://openalex.org/W4295094535","https://openalex.org/W4283583523","https://openalex.org/W4291914418","https://openalex.org/W4214624958","https://openalex.org/W4289075993","https://openalex.org/W1548220668"],"abstract_inverted_index":{"In":[0],"this":[1,28,33],"paper,":[2],"we":[3],"consider":[4],"the":[5,22,36,48,62],"generalized":[6],"linear":[7],"complementarily":[8],"problem":[9,29],"VLCP":[10],"$(q,A)$":[11],"where":[12],"A":[13],"is":[14,76],"a":[15,42,58,71,77],"vertical":[16,73,78],"block":[17,74,79],"Z-matrix.":[18],"We":[19,54],"prove":[20],"that":[21,32,41,57],"Cottle\u2013Dantzig":[23,63],"pivoting":[24],"algorithm":[25,34,45,64],"can":[26,65],"process":[27],"by":[30],"showing":[31],"generates":[35],"same":[37],"sequence":[38],"of":[39,61],"bases":[40],"modified":[43,59],"simplex":[44],"for":[46,68],"minimizing":[47],"artificial":[49],"variable":[50],"$z_0":[51],"$":[52],"does.":[53],"also":[55],"show":[56],"version":[60],"be":[66],"used":[67],"determining":[69],"whether":[70],"given":[72],"Z-matrix":[75],"$P_0":[80],"$-matrix.":[81]},"counts_by_year":[{"year":2026,"cited_by_count":3},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}