{"id":"https://openalex.org/W2004467349","doi":"https://doi.org/10.1007/bf01585770","title":"A unified approach to global convergence of trust region methods for nonsmooth optimization","display_name":"A unified approach to global convergence of trust region methods for nonsmooth optimization","publication_year":1995,"publication_date":"1995-01-01","ids":{"openalex":"https://openalex.org/W2004467349","doi":"https://doi.org/10.1007/bf01585770","mag":"2004467349"},"language":"en","primary_location":{"id":"doi:10.1007/bf01585770","is_oa":false,"landing_page_url":"https://doi.org/10.1007/bf01585770","pdf_url":null,"source":{"id":"https://openalex.org/S193920097","display_name":"Mathematical Programming","issn_l":"0025-5610","issn":["0025-5610","1436-4646"],"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":"Mathematical Programming","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/A5109961247","display_name":"J. E. Dennis","orcid":null},"institutions":[{"id":"https://openalex.org/I74775410","display_name":"Rice University","ror":"https://ror.org/008zs3103","country_code":"US","type":"education","lineage":["https://openalex.org/I74775410"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"John E. Dennis","raw_affiliation_strings":["Department of Computational and Applied Mathematics and Center for Research on Parallel Computation, Rice University, 77251-1892, Houston, TX, USA","Department of Computational and Applied Mathematics and Center for Research on Parallel Computation, Rice University, Houston, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computational and Applied Mathematics and Center for Research on Parallel Computation, Rice University, 77251-1892, Houston, TX, USA","institution_ids":["https://openalex.org/I74775410"]},{"raw_affiliation_string":"Department of Computational and Applied Mathematics and Center for Research on Parallel Computation, Rice University, Houston, USA","institution_ids":["https://openalex.org/I74775410"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5033274466","display_name":"Shou-Bai B. Li","orcid":null},"institutions":[{"id":"https://openalex.org/I74775410","display_name":"Rice University","ror":"https://ror.org/008zs3103","country_code":"US","type":"education","lineage":["https://openalex.org/I74775410"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Shou-Bai B. Li","raw_affiliation_strings":["Department of Computational and Applied Mathematics and Center for Research on Parallel Computation, Rice University, 77251-1892, Houston, TX, USA","Department of Computational and Applied Mathematics and Center for Research on Parallel Computation, Rice University, Houston, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computational and Applied Mathematics and Center for Research on Parallel Computation, Rice University, 77251-1892, Houston, TX, USA","institution_ids":["https://openalex.org/I74775410"]},{"raw_affiliation_string":"Department of Computational and Applied Mathematics and Center for Research on Parallel Computation, Rice University, Houston, USA","institution_ids":["https://openalex.org/I74775410"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5108338956","display_name":"R. A. Tapia","orcid":null},"institutions":[{"id":"https://openalex.org/I74775410","display_name":"Rice University","ror":"https://ror.org/008zs3103","country_code":"US","type":"education","lineage":["https://openalex.org/I74775410"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Richard A. Tapia","raw_affiliation_strings":["Department of Computational and Applied Mathematics and Center for Research on Parallel Computation, Rice University, 77251-1892, Houston, TX, USA","Department of Computational and Applied Mathematics and Center for Research on Parallel Computation, Rice University, Houston, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computational and Applied Mathematics and Center for Research on Parallel Computation, Rice University, 77251-1892, Houston, TX, USA","institution_ids":["https://openalex.org/I74775410"]},{"raw_affiliation_string":"Department of Computational and Applied Mathematics and Center for Research on Parallel Computation, Rice University, Houston, USA","institution_ids":["https://openalex.org/I74775410"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I74775410"],"apc_list":{"value":2890,"currency":"USD","value_usd":2890},"apc_paid":null,"fwci":2.6422,"has_fulltext":false,"cited_by_count":50,"citation_normalized_percentile":{"value":0.88703527,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"68","issue":"1-3","first_page":"319","last_page":"346"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9998999834060669,"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":0.9998999834060669,"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/T10792","display_name":"Matrix Theory and Algorithms","score":0.996399998664856,"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":0.9919000267982483,"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/mathematics","display_name":"Mathematics","score":0.8137012720108032},{"id":"https://openalex.org/keywords/trust-region","display_name":"Trust region","score":0.6954642534255981},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.6838643550872803},{"id":"https://openalex.org/keywords/nonlinear-programming","display_name":"Nonlinear programming","score":0.5950555205345154},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.57668536901474},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.5711458325386047},{"id":"https://openalex.org/keywords/local-convergence","display_name":"Local convergence","score":0.5156756639480591},{"id":"https://openalex.org/keywords/symbolic-convergence-theory","display_name":"Symbolic convergence theory","score":0.44230878353118896},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.4371154308319092},{"id":"https://openalex.org/keywords/minification","display_name":"Minification","score":0.43710651993751526},{"id":"https://openalex.org/keywords/optimization-problem","display_name":"Optimization problem","score":0.4330032169818878},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3868609368801117},{"id":"https://openalex.org/keywords/iterative-method","display_name":"Iterative method","score":0.17692908644676208},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.1587125062942505}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8137012720108032},{"id":"https://openalex.org/C89109886","wikidata":"https://www.wikidata.org/wiki/Q1535924","display_name":"Trust region","level":3,"score":0.6954642534255981},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.6838643550872803},{"id":"https://openalex.org/C115527620","wikidata":"https://www.wikidata.org/wiki/Q769909","display_name":"Nonlinear programming","level":3,"score":0.5950555205345154},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.57668536901474},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5711458325386047},{"id":"https://openalex.org/C117898588","wikidata":"https://www.wikidata.org/wiki/Q6664310","display_name":"Local convergence","level":3,"score":0.5156756639480591},{"id":"https://openalex.org/C64980692","wikidata":"https://www.wikidata.org/wiki/Q16191959","display_name":"Symbolic convergence theory","level":3,"score":0.44230878353118896},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.4371154308319092},{"id":"https://openalex.org/C147764199","wikidata":"https://www.wikidata.org/wiki/Q6865248","display_name":"Minification","level":2,"score":0.43710651993751526},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.4330032169818878},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3868609368801117},{"id":"https://openalex.org/C159694833","wikidata":"https://www.wikidata.org/wiki/Q2321565","display_name":"Iterative method","level":2,"score":0.17692908644676208},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.1587125062942505},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0},{"id":"https://openalex.org/C178635117","wikidata":"https://www.wikidata.org/wiki/Q747499","display_name":"RADIUS","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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C26517878","wikidata":"https://www.wikidata.org/wiki/Q228039","display_name":"Key (lock)","level":2,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C38652104","wikidata":"https://www.wikidata.org/wiki/Q3510521","display_name":"Computer security","level":1,"score":0.0},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1007/bf01585770","is_oa":false,"landing_page_url":"https://doi.org/10.1007/bf01585770","pdf_url":null,"source":{"id":"https://openalex.org/S193920097","display_name":"Mathematical Programming","issn_l":"0025-5610","issn":["0025-5610","1436-4646"],"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":"Mathematical Programming","raw_type":"journal-article"},{"id":"pmh:ADA455260","is_oa":false,"landing_page_url":"http://oai.dtic.mil/oai/oai?&amp;verb=getRecord&amp;metadataPrefix=html&amp;identifier=ADA455260","pdf_url":null,"source":{"id":"https://openalex.org/S4406923043","display_name":"Defense Technical Information Center (DTIC)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"DTIC","raw_type":"Text"},{"id":"pmh:oai:repository.rice.edu:1911/101657","is_oa":false,"landing_page_url":"https://hdl.handle.net/1911/101657&quot;&gt;https://hdl.handle.net/1911/101657&lt;/a&gt;.","pdf_url":null,"source":{"id":"https://openalex.org/S4306401268","display_name":"Rice Digital Scholarship Archive (Rice University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I74775410","host_organization_name":"Rice University","host_organization_lineage":["https://openalex.org/I74775410"],"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"},{"id":"pmh:oai:scholarship.rice.edu:1911/101657","is_oa":false,"landing_page_url":"http://hdl.handle.net/1911/101657","pdf_url":null,"source":{"id":"https://openalex.org/S4306401268","display_name":"Rice Digital Scholarship Archive (Rice University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I74775410","host_organization_name":"Rice University","host_organization_lineage":["https://openalex.org/I74775410"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Technical report"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320338281","display_name":"Army Research Office","ror":"https://ror.org/05epdh915"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":17,"referenced_works":["https://openalex.org/W170686111","https://openalex.org/W275685090","https://openalex.org/W1586015540","https://openalex.org/W1893275031","https://openalex.org/W1964009395","https://openalex.org/W2006420513","https://openalex.org/W2068484625","https://openalex.org/W2077658674","https://openalex.org/W2090963365","https://openalex.org/W2094879958","https://openalex.org/W2119842211","https://openalex.org/W2581683888","https://openalex.org/W3012317737","https://openalex.org/W4212997115","https://openalex.org/W4249667877","https://openalex.org/W4251416849","https://openalex.org/W4299512035"],"related_works":["https://openalex.org/W2386509554","https://openalex.org/W2050613758","https://openalex.org/W1555927645","https://openalex.org/W2352071214","https://openalex.org/W2119283772","https://openalex.org/W1548320777","https://openalex.org/W2098918699","https://openalex.org/W2080003833","https://openalex.org/W2058475249","https://openalex.org/W2351080754"],"abstract_inverted_index":null,"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":2},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":3},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":1},{"year":2015,"cited_by_count":9},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":2}],"updated_date":"2026-08-15T07:11:24.734988","created_date":"2025-10-10T00:00:00"}
