{"id":"https://openalex.org/W2001024683","doi":"https://doi.org/10.1080/10556789508805606","title":"The path solver: a nommonotone stabilization scheme for mixed complementarity problems","display_name":"The path solver: a nommonotone stabilization scheme for mixed complementarity problems","publication_year":1995,"publication_date":"1995-01-01","ids":{"openalex":"https://openalex.org/W2001024683","doi":"https://doi.org/10.1080/10556789508805606","mag":"2001024683"},"language":"en","primary_location":{"id":"doi:10.1080/10556789508805606","doi":"https://doi.org/10.1080/10556789508805606","is_oa":false,"landing_page_url":"https://doi.org/10.1080/10556789508805606","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,"listed_in":["anvur-scientific","cwts-core","dongbi-b","jufo-1","norway-1","poland-70","russia-white-list-1"],"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547","https://openalex.org/P4310320449"],"host_organization_lineage_names":["Taylor & Francis","Informa"],"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"},"volume":null,"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/A5005814980","display_name":"Steven P. Dirkse","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I135310074","display_name":"University of Wisconsin\u2013Madison","ror":"https://ror.org/01y2jtd41","country_code":"US","type":"education","lineage":["https://openalex.org/I135310074"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Steven P. Dirkse","raw_affiliation_strings":["Computer Sciences Department, University of Wisconsin, Madison, Wisconsin, 53706, USA","Computer Sciences Department University of Wisconsin Madison, Wisconsin 53706, USA#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Computer Sciences Department, University of Wisconsin, Madison, Wisconsin, 53706, USA","institution_ids":["https://openalex.org/I135310074"]},{"raw_affiliation_string":"Computer Sciences Department University of Wisconsin Madison, Wisconsin 53706, USA#TAB#","institution_ids":["https://openalex.org/I135310074"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5088455558","display_name":"Michael C. Ferris","orcid":"https://orcid.org/0000-0002-7652-6776","observed_orcids":["https://orcid.org/0000-0002-7652-6776"]},"institutions":[{"id":"https://openalex.org/I135310074","display_name":"University of Wisconsin\u2013Madison","ror":"https://ror.org/01y2jtd41","country_code":"US","type":"education","lineage":["https://openalex.org/I135310074"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Michael C. Ferris","raw_affiliation_strings":["Computer Sciences Department, University of Wisconsin, Madison, Wisconsin, 53706, USA","Computer Sciences Department University of Wisconsin Madison, Wisconsin 53706, USA#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Computer Sciences Department, University of Wisconsin, Madison, Wisconsin, 53706, USA","institution_ids":["https://openalex.org/I135310074"]},{"raw_affiliation_string":"Computer Sciences Department University of Wisconsin Madison, Wisconsin 53706, USA#TAB#","institution_ids":["https://openalex.org/I135310074"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I135310074"],"apc_list":null,"apc_paid":null,"fwci":18.0312,"has_fulltext":false,"cited_by_count":730,"citation_normalized_percentile":{"value":0.99876007,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":99,"max":100},"biblio":{"volume":"5","issue":"2","first_page":"123","last_page":"156"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.7875999808311462,"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":0.7875999808311462,"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":0.20479999482631683,"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/T12661","display_name":"Iterative Methods for Nonlinear Equations","score":0.003000000026077032,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mixed-complementarity-problem","display_name":"mixed complementarity problem","score":0.8769999742507935},{"id":"https://openalex.org/keywords/path-generation","display_name":"path generation","score":0.8379999995231628},{"id":"https://openalex.org/keywords/piecewise-linear-paths","display_name":"piecewise linear paths","score":0.8240000009536743},{"id":"https://openalex.org/keywords/global-convergence","display_name":"global convergence","score":0.8830000162124634},{"id":"https://openalex.org/keywords/nonlinear-complementarity-problem","display_name":"nonlinear complementarity problem","score":0.6019999980926514}],"concepts":[{"id":"https://openalex.org/C2778770139","wikidata":"https://www.wikidata.org/wiki/Q1966904","display_name":"Solver","level":2,"score":0.8005638122558594},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7456319332122803},{"id":"https://openalex.org/C2834757","wikidata":"https://www.wikidata.org/wiki/Q4925424","display_name":"Monotone polygon","level":2,"score":0.6916395425796509},{"id":"https://openalex.org/C202269582","wikidata":"https://www.wikidata.org/wiki/Q2644277","display_name":"Complementarity (molecular biology)","level":2,"score":0.6623015403747559},{"id":"https://openalex.org/C2777735758","wikidata":"https://www.wikidata.org/wiki/Q817765","display_name":"Path (computing)","level":2,"score":0.6259855031967163},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.608695387840271},{"id":"https://openalex.org/C164660894","wikidata":"https://www.wikidata.org/wiki/Q2037833","display_name":"Piecewise","level":2,"score":0.5489826202392578},{"id":"https://openalex.org/C155253501","wikidata":"https://www.wikidata.org/wiki/Q461992","display_name":"Interior point method","level":2,"score":0.5193882584571838},{"id":"https://openalex.org/C77618280","wikidata":"https://www.wikidata.org/wiki/Q1155772","display_name":"Scheme (mathematics)","level":2,"score":0.4893741011619568},{"id":"https://openalex.org/C2778646529","wikidata":"https://www.wikidata.org/wiki/Q16948724","display_name":"Nonlinear complementarity problem","level":4,"score":0.4864315986633301},{"id":"https://openalex.org/C34320192","wikidata":"https://www.wikidata.org/wiki/Q783105","display_name":"Linear complementarity problem","level":3,"score":0.48079243302345276},{"id":"https://openalex.org/C17095337","wikidata":"https://www.wikidata.org/wiki/Q2375229","display_name":"Piecewise linear function","level":2,"score":0.42413896322250366},{"id":"https://openalex.org/C85404239","wikidata":"https://www.wikidata.org/wiki/Q5156417","display_name":"Complementarity theory","level":3,"score":0.39499014616012573},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3600916564464569},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.20430424809455872},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.1743147075176239},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.07166779041290283},{"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/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C54355233","wikidata":"https://www.wikidata.org/wiki/Q7162","display_name":"Genetics","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/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1080/10556789508805606","doi":"https://doi.org/10.1080/10556789508805606","is_oa":false,"landing_page_url":"https://doi.org/10.1080/10556789508805606","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,"listed_in":["anvur-scientific","cwts-core","dongbi-b","jufo-1","norway-1","poland-70","russia-white-list-1"],"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547","https://openalex.org/P4310320449"],"host_organization_lineage_names":["Taylor & Francis","Informa"],"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"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.34.3976","doi":null,"is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.34.3976","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"ftp://ftp.cs.wisc.edu/tech-reports/reports/1993/tr1179.ps","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.49.9190","doi":null,"is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.49.9190","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"ftp://ftp.cs.wisc.edu/tech-reports/reports/93/tr1179.ps","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.651.8889","doi":null,"is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.651.8889","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://pages.cs.wisc.edu/%7Eferris/techreports/cstr1179.pdf","raw_type":"text"},{"id":"pmh:oai:minds.wisc.edu:1793/59786","doi":null,"is_oa":false,"landing_page_url":"http://digital.library.wisc.edu/1793/59786","pdf_url":null,"source":{"id":"https://openalex.org/S4306401622","display_name":"Minds at UW (University of Wisconsin)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I135310074","host_organization_name":"University of Wisconsin\u2013Madison","host_organization_lineage":["https://openalex.org/I135310074"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Technical Report"}],"best_oa_location":null,"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":51,"referenced_works":["https://openalex.org/W82221089","https://openalex.org/W84056083","https://openalex.org/W653822251","https://openalex.org/W1484204181","https://openalex.org/W1519983908","https://openalex.org/W1528330203","https://openalex.org/W1565639511","https://openalex.org/W1597988518","https://openalex.org/W1969811075","https://openalex.org/W1972378233","https://openalex.org/W1977904123","https://openalex.org/W1978001564","https://openalex.org/W1982027431","https://openalex.org/W1985229624","https://openalex.org/W1993647205","https://openalex.org/W1999560964","https://openalex.org/W2000598349","https://openalex.org/W2004936497","https://openalex.org/W2007331580","https://openalex.org/W2007753746","https://openalex.org/W2009388515","https://openalex.org/W2013327579","https://openalex.org/W2038178878","https://openalex.org/W2043430160","https://openalex.org/W2045622192","https://openalex.org/W2047382992","https://openalex.org/W2047558828","https://openalex.org/W2050864977","https://openalex.org/W2053643774","https://openalex.org/W2059635037","https://openalex.org/W2068484625","https://openalex.org/W2077658674","https://openalex.org/W2079917093","https://openalex.org/W2090963365","https://openalex.org/W2093246563","https://openalex.org/W2095117927","https://openalex.org/W2118700449","https://openalex.org/W2152122625","https://openalex.org/W2162916973","https://openalex.org/W2166161964","https://openalex.org/W2290441346","https://openalex.org/W2731844756","https://openalex.org/W2913384691","https://openalex.org/W2994673811","https://openalex.org/W3012317737","https://openalex.org/W3145383118","https://openalex.org/W3215365563","https://openalex.org/W4212997115","https://openalex.org/W4247264753","https://openalex.org/W4285719527","https://openalex.org/W4299512035"],"related_works":["https://openalex.org/W7100713658","https://openalex.org/W7005129446","https://openalex.org/W7096471197","https://openalex.org/W7098571031","https://openalex.org/W7071161792","https://openalex.org/W61778493","https://openalex.org/W7047053029","https://openalex.org/W947217487","https://openalex.org/W7095244289","https://openalex.org/W1990220583"],"abstract_inverted_index":{"The":[0,19,59],"PATH":[1],"solver":[2],"is":[3,27,61],"an":[4],"implementation":[5],"of":[6,14],"a":[7,23,31,42,48],"stabilized":[8],"Newton":[9,40],"method":[10],"for":[11],"the":[12,15,35,39,56,78,96],"solution":[13],"Mixed":[16],"Complementarity":[17],"Problem.":[18],"stabilization":[20],"scheme":[21],"employs":[22],"path-generation":[24],"procedure":[25],"which":[26,69],"used":[28,53],"to":[29,38,54,63,73],"construct":[30],"piecewise-linear":[32],"path":[33],"from":[34,91],"current":[36],"point":[37],"point;":[41],"step":[43],"length":[44],"acceptance":[45],"criterion":[46],"and":[47,86],"non-monotone":[49],"pathsearch":[50],"are":[51,84,98],"then":[52],"choose":[55],"next":[57],"iterate.":[58],"algorithm":[60],"shown":[62],"be":[64],"globally":[65],"convergent":[66],"under":[67],"assumptions":[68],"generalize":[70],"those":[71],"required":[72],"obtain":[74],"similar":[75],"results":[76,89],"in":[77,95],"smooth":[79],"case.":[80],"Several":[81],"imple\u03adentation":[82],"issues":[83],"discussed,":[85],"extensive":[87],"computational":[88],"obtained":[90],"problems":[92],"commonly":[93],"found":[94],"literature":[97],"given":[99]},"counts_by_year":[{"year":2026,"cited_by_count":20},{"year":2025,"cited_by_count":23},{"year":2024,"cited_by_count":20},{"year":2023,"cited_by_count":22},{"year":2022,"cited_by_count":22},{"year":2021,"cited_by_count":16},{"year":2020,"cited_by_count":21},{"year":2019,"cited_by_count":27},{"year":2018,"cited_by_count":21},{"year":2017,"cited_by_count":27},{"year":2016,"cited_by_count":29},{"year":2015,"cited_by_count":23},{"year":2014,"cited_by_count":32},{"year":2013,"cited_by_count":33},{"year":2012,"cited_by_count":34}],"updated_date":"2026-11-04T10:54:05.112534","created_date":"2016-06-24T00:00:00"}
