{"id":"https://openalex.org/W1998163691","doi":"https://doi.org/10.1007/s10898-014-0206-y","title":"A new semi-smooth Newton multigrid method for control-constrained semi-linear elliptic PDE problems","display_name":"A new semi-smooth Newton multigrid method for control-constrained semi-linear elliptic PDE problems","publication_year":2014,"publication_date":"2014-06-08","ids":{"openalex":"https://openalex.org/W1998163691","doi":"https://doi.org/10.1007/s10898-014-0206-y","mag":"1998163691"},"language":"en","primary_location":{"id":"doi:10.1007/s10898-014-0206-y","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10898-014-0206-y","pdf_url":null,"source":{"id":"https://openalex.org/S115925768","display_name":"Journal of Global Optimization","issn_l":"0925-5001","issn":["0925-5001","1573-2916"],"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":"Journal of Global 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/A5100362043","display_name":"Jun Liu","orcid":"https://orcid.org/0009-0004-8026-3704"},"institutions":[{"id":"https://openalex.org/I110378019","display_name":"Southern Illinois University Carbondale","ror":"https://ror.org/049kefs16","country_code":"US","type":"education","lineage":["https://openalex.org/I110378019","https://openalex.org/I2801502357"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Jun Liu","raw_affiliation_strings":["Department of Mathematics, Southern Illinois University, Carbondale, Illinois, \u00a062901, USA","Department of Mathematics, Southern Illinois University, Carbondale, USA 62901"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Southern Illinois University, Carbondale, Illinois, \u00a062901, USA","institution_ids":["https://openalex.org/I110378019"]},{"raw_affiliation_string":"Department of Mathematics, Southern Illinois University, Carbondale, USA 62901","institution_ids":["https://openalex.org/I110378019"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5008007155","display_name":"Mingqing Xiao","orcid":"https://orcid.org/0000-0003-3241-4112"},"institutions":[{"id":"https://openalex.org/I110378019","display_name":"Southern Illinois University Carbondale","ror":"https://ror.org/049kefs16","country_code":"US","type":"education","lineage":["https://openalex.org/I110378019","https://openalex.org/I2801502357"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Mingqing Xiao","raw_affiliation_strings":["Department of Mathematics, Southern Illinois University, Carbondale, Illinois, \u00a062901, USA","Department of Mathematics, Southern Illinois University, Carbondale, USA 62901"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Southern Illinois University, Carbondale, Illinois, \u00a062901, USA","institution_ids":["https://openalex.org/I110378019"]},{"raw_affiliation_string":"Department of Mathematics, Southern Illinois University, Carbondale, USA 62901","institution_ids":["https://openalex.org/I110378019"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5100362043"],"corresponding_institution_ids":["https://openalex.org/I110378019"],"apc_list":{"value":2190,"currency":"EUR","value_usd":2780},"apc_paid":null,"fwci":1.9293,"has_fulltext":false,"cited_by_count":8,"citation_normalized_percentile":{"value":0.84037911,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"64","issue":"3","first_page":"451","last_page":"468"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9998000264167786,"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"}},"topics":[{"id":"https://openalex.org/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9998000264167786,"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"}},{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9993000030517578,"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":0.9976999759674072,"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/multigrid-method","display_name":"Multigrid method","score":0.8677524328231812},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.75729900598526},{"id":"https://openalex.org/keywords/jacobian-matrix-and-determinant","display_name":"Jacobian matrix and determinant","score":0.6480388045310974},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.6142902970314026},{"id":"https://openalex.org/keywords/solver","display_name":"Solver","score":0.542064905166626},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5395826697349548},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.4310375154018402},{"id":"https://openalex.org/keywords/newtons-method","display_name":"Newton's method","score":0.41493844985961914},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.41195201873779297},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.41033071279525757},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.25086766481399536},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.2119472324848175}],"concepts":[{"id":"https://openalex.org/C137119250","wikidata":"https://www.wikidata.org/wiki/Q1413101","display_name":"Multigrid method","level":3,"score":0.8677524328231812},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.75729900598526},{"id":"https://openalex.org/C200331156","wikidata":"https://www.wikidata.org/wiki/Q506041","display_name":"Jacobian matrix and determinant","level":2,"score":0.6480388045310974},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.6142902970314026},{"id":"https://openalex.org/C2778770139","wikidata":"https://www.wikidata.org/wiki/Q1966904","display_name":"Solver","level":2,"score":0.542064905166626},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5395826697349548},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4310375154018402},{"id":"https://openalex.org/C85189116","wikidata":"https://www.wikidata.org/wiki/Q374195","display_name":"Newton's method","level":3,"score":0.41493844985961914},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.41195201873779297},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.41033071279525757},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.25086766481399536},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2119472324848175},{"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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1007/s10898-014-0206-y","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10898-014-0206-y","pdf_url":null,"source":{"id":"https://openalex.org/S115925768","display_name":"Journal of Global Optimization","issn_l":"0925-5001","issn":["0925-5001","1573-2916"],"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":"Journal of Global Optimization","raw_type":"journal-article"},{"id":"pmh:oai:RePEc:spr:jglopt:v:64:y:2016:i:3:d:10.1007_s10898-014-0206-y","is_oa":false,"landing_page_url":"http://link.springer.com/10.1007/s10898-014-0206-y","pdf_url":null,"source":{"id":"https://openalex.org/S4306401271","display_name":"RePEc: Research Papers in Economics","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I77793887","host_organization_name":"Federal Reserve Bank of St. Louis","host_organization_lineage":["https://openalex.org/I77793887"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"article"},{"id":"pmh:oai:RePEc:spr:jglopt:v:64:y:2016:i:3:p:451-468","is_oa":false,"landing_page_url":"http://hdl.handle.net/10.1007/s10898-014-0206-y","pdf_url":null,"source":{"id":"https://openalex.org/S4306401271","display_name":"RePEc: Research Papers in Economics","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I77793887","host_organization_name":"Federal Reserve Bank of St. Louis","host_organization_lineage":["https://openalex.org/I77793887"],"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":"article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":45,"referenced_works":["https://openalex.org/W40037269","https://openalex.org/W433418221","https://openalex.org/W581038412","https://openalex.org/W594510519","https://openalex.org/W1506342804","https://openalex.org/W1530872699","https://openalex.org/W1542744440","https://openalex.org/W1559687661","https://openalex.org/W1579781026","https://openalex.org/W1600371943","https://openalex.org/W1820125862","https://openalex.org/W1974791647","https://openalex.org/W1977135073","https://openalex.org/W1978837662","https://openalex.org/W1989116194","https://openalex.org/W1992056335","https://openalex.org/W1997542937","https://openalex.org/W2009134079","https://openalex.org/W2022977680","https://openalex.org/W2026365342","https://openalex.org/W2026938587","https://openalex.org/W2053514102","https://openalex.org/W2055102513","https://openalex.org/W2059991864","https://openalex.org/W2064180255","https://openalex.org/W2069326267","https://openalex.org/W2071431995","https://openalex.org/W2079482881","https://openalex.org/W2085581918","https://openalex.org/W2086517326","https://openalex.org/W2087003257","https://openalex.org/W2090963365","https://openalex.org/W2105253623","https://openalex.org/W2107501462","https://openalex.org/W2115178538","https://openalex.org/W2123982001","https://openalex.org/W2129121555","https://openalex.org/W2139081976","https://openalex.org/W2141870784","https://openalex.org/W2151317657","https://openalex.org/W2488897645","https://openalex.org/W2610857016","https://openalex.org/W4230278521","https://openalex.org/W4285719527","https://openalex.org/W4298228534"],"related_works":["https://openalex.org/W4283689850","https://openalex.org/W2480676685","https://openalex.org/W2501988474","https://openalex.org/W2145985977","https://openalex.org/W2021837978","https://openalex.org/W857380701","https://openalex.org/W1693001741","https://openalex.org/W2031857480","https://openalex.org/W2090289299","https://openalex.org/W252197264"],"abstract_inverted_index":null,"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":3},{"year":2014,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}