{"id":"https://openalex.org/W2084556800","doi":"https://doi.org/10.1137/51052623496311880","title":"A Nonlinear Analytic Center Cutting Plane Method for a Class of Convex Programming Problems","display_name":"A Nonlinear Analytic Center Cutting Plane Method for a Class of Convex Programming Problems","publication_year":1998,"publication_date":"1998-11-01","ids":{"openalex":"https://openalex.org/W2084556800","doi":"https://doi.org/10.1137/51052623496311880","mag":"2084556800"},"language":"en","primary_location":{"id":"doi:10.1137/51052623496311880","is_oa":false,"landing_page_url":"https://doi.org/10.1137/51052623496311880","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/A5082357948","display_name":"Faranak Sharifi Mokhtarian","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"F. Sharifi Mokhtarian","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5081792425","display_name":"Jean\u2010Louis Goffin","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"J. L. Goffin","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.6605,"has_fulltext":false,"cited_by_count":21,"citation_normalized_percentile":{"value":0.90650214,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"8","issue":"4","first_page":"1108","last_page":"1131"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9993000030517578,"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":0.9993000030517578,"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/T12176","display_name":"Optimization and Packing Problems","score":0.9984999895095825,"subfield":{"id":"https://openalex.org/subfields/2209","display_name":"Industrial and Manufacturing Engineering"},"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/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9958000183105469,"subfield":{"id":"https://openalex.org/subfields/1704","display_name":"Computer Graphics and Computer-Aided Design"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8339059352874756},{"id":"https://openalex.org/keywords/cutting-plane-method","display_name":"Cutting-plane method","score":0.7357907295227051},{"id":"https://openalex.org/keywords/polytope","display_name":"Polytope","score":0.7015953063964844},{"id":"https://openalex.org/keywords/intersection","display_name":"Intersection (aeronautics)","score":0.6282216310501099},{"id":"https://openalex.org/keywords/feasible-region","display_name":"Feasible region","score":0.5864807367324829},{"id":"https://openalex.org/keywords/nonlinear-programming","display_name":"Nonlinear programming","score":0.5641993284225464},{"id":"https://openalex.org/keywords/convex-polytope","display_name":"Convex polytope","score":0.4787811040878296},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.46433010697364807},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.45915475487709045},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.44869402050971985},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.4350399374961853},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.4004257917404175},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.33706074953079224},{"id":"https://openalex.org/keywords/convex-set","display_name":"Convex set","score":0.32079824805259705},{"id":"https://openalex.org/keywords/convex-optimization","display_name":"Convex optimization","score":0.30413007736206055},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.1470595896244049},{"id":"https://openalex.org/keywords/integer-programming","display_name":"Integer programming","score":0.1338009536266327}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8339059352874756},{"id":"https://openalex.org/C109839438","wikidata":"https://www.wikidata.org/wiki/Q1762039","display_name":"Cutting-plane method","level":3,"score":0.7357907295227051},{"id":"https://openalex.org/C145691206","wikidata":"https://www.wikidata.org/wiki/Q747980","display_name":"Polytope","level":2,"score":0.7015953063964844},{"id":"https://openalex.org/C64543145","wikidata":"https://www.wikidata.org/wiki/Q162942","display_name":"Intersection (aeronautics)","level":2,"score":0.6282216310501099},{"id":"https://openalex.org/C177067428","wikidata":"https://www.wikidata.org/wiki/Q17013331","display_name":"Feasible region","level":2,"score":0.5864807367324829},{"id":"https://openalex.org/C115527620","wikidata":"https://www.wikidata.org/wiki/Q769909","display_name":"Nonlinear programming","level":3,"score":0.5641993284225464},{"id":"https://openalex.org/C110943637","wikidata":"https://www.wikidata.org/wiki/Q4129097","display_name":"Convex polytope","level":5,"score":0.4787811040878296},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.46433010697364807},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.45915475487709045},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.44869402050971985},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.4350399374961853},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.4004257917404175},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.33706074953079224},{"id":"https://openalex.org/C49870271","wikidata":"https://www.wikidata.org/wiki/Q193657","display_name":"Convex set","level":4,"score":0.32079824805259705},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.30413007736206055},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.1470595896244049},{"id":"https://openalex.org/C56086750","wikidata":"https://www.wikidata.org/wiki/Q6042592","display_name":"Integer programming","level":2,"score":0.1338009536266327},{"id":"https://openalex.org/C146978453","wikidata":"https://www.wikidata.org/wiki/Q3798668","display_name":"Aerospace engineering","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/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"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/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1137/51052623496311880","is_oa":false,"landing_page_url":"https://doi.org/10.1137/51052623496311880","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"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.31.5820","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.31.5820","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"ftp://ftp.crt.umontreal.ca/pub/users/jlg/siampape.ps.gz","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.54.952","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.54.952","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"ftp://ftp.crt.umontreal.ca/pub/users/jlg/G-96-53.ps.gz","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":30,"referenced_works":["https://openalex.org/W171180563","https://openalex.org/W1514645957","https://openalex.org/W1533092490","https://openalex.org/W1632601927","https://openalex.org/W1966986674","https://openalex.org/W1967150773","https://openalex.org/W1972691999","https://openalex.org/W1980331059","https://openalex.org/W1993982015","https://openalex.org/W2045068465","https://openalex.org/W2048133466","https://openalex.org/W2050798859","https://openalex.org/W2054090890","https://openalex.org/W2054876264","https://openalex.org/W2059499240","https://openalex.org/W2064948689","https://openalex.org/W2070426678","https://openalex.org/W2081632040","https://openalex.org/W2081807695","https://openalex.org/W2084556800","https://openalex.org/W2087338175","https://openalex.org/W2095365233","https://openalex.org/W2161182482","https://openalex.org/W2341541053","https://openalex.org/W2561178549","https://openalex.org/W4231459397","https://openalex.org/W4233177862","https://openalex.org/W4235328454","https://openalex.org/W4237512656","https://openalex.org/W4251460852"],"related_works":["https://openalex.org/W1990911204","https://openalex.org/W2069107464","https://openalex.org/W2768257653","https://openalex.org/W2557288725","https://openalex.org/W3012067785","https://openalex.org/W4243575619","https://openalex.org/W1607687497","https://openalex.org/W4288640859","https://openalex.org/W2045384787","https://openalex.org/W940482830"],"abstract_inverted_index":{"A":[0],"cutting":[1],"plane":[2],"algorithm":[3,20],"for":[4],"minimizing":[5],"a":[6,14,44,55,59,74,78,120],"convex":[7],"function":[8,32],"subject":[9],"to":[10],"constraints":[11],"defined":[12],"by":[13,43,53],"separation":[15],"oracle":[16],"is":[17,21,33,41,50,65,96],"presented.":[18],"The":[19,27],"based":[22],"on":[23,116],"approximate":[24,67,109],"analytic":[25,68],"centers.":[26],"nonlinearity":[28],"of":[29,70,73,81,90,100,107,119,123],"the":[30,38,71,82,88,91,101,104,117,124],"objective":[31,84],"taken":[34],"into":[35],"account,":[36],"yet":[37],"feasible":[39],"region":[40],"approximated":[42],"containing":[45,48,75],"polytope.":[46],"This":[47],"polytope":[49,76],"regularly":[51],"updated":[52],"adding":[54],"new":[56],"cut":[57],"through":[58],"test":[60,63],"point.":[61],"Each":[62],"point":[64],"an":[66,108],"center":[69],"intersection":[72],"and":[77,111],"level":[79],"set":[80],"nonlinear":[83],"function.":[85],"We":[86],"establish":[87],"complexity":[89,94],"algorithm.":[92],"Our":[93],"estimate":[95],"given":[97],"in":[98],"terms":[99],"problem":[102],"dimension,":[103],"desired":[105],"accuracy":[106],"solution,":[110],"other":[112],"parameters":[113],"that":[114],"depend":[115],"geometry":[118],"specific":[121],"instance":[122],"problem.":[125]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":2},{"year":2013,"cited_by_count":1}],"updated_date":"2026-08-26T07:47:46.906454","created_date":"2025-10-10T00:00:00"}
