{"id":"https://openalex.org/W2125968326","doi":"https://doi.org/10.1007/s10898-008-9373-z","title":"Some characterizations for SOC-monotone and SOC-convex functions","display_name":"Some characterizations for SOC-monotone and SOC-convex functions","publication_year":2008,"publication_date":"2008-11-06","ids":{"openalex":"https://openalex.org/W2125968326","doi":"https://doi.org/10.1007/s10898-008-9373-z","mag":"2125968326"},"language":"en","primary_location":{"id":"doi:10.1007/s10898-008-9373-z","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10898-008-9373-z","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/A5061633817","display_name":"Jein-Shan Chen","orcid":"https://orcid.org/0000-0002-4596-9419"},"institutions":[{"id":"https://openalex.org/I134161618","display_name":"National Taiwan Normal University","ror":"https://ror.org/059dkdx38","country_code":"TW","type":"education","lineage":["https://openalex.org/I134161618"]}],"countries":["TW"],"is_corresponding":true,"raw_author_name":"Jein-Shan Chen","raw_affiliation_strings":["Department of Mathematics, National Taiwan Normal University, Taipei, 11677, Taiwan","Department of Mathematics, National Taiwan Normal University, Taipei, Taiwan 11677"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, National Taiwan Normal University, Taipei, 11677, Taiwan","institution_ids":["https://openalex.org/I134161618"]},{"raw_affiliation_string":"Department of Mathematics, National Taiwan Normal University, Taipei, Taiwan 11677","institution_ids":["https://openalex.org/I134161618"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100363077","display_name":"Xin Chen","orcid":"https://orcid.org/0000-0002-5168-4823"},"institutions":[{"id":"https://openalex.org/I157725225","display_name":"University of Illinois Urbana-Champaign","ror":"https://ror.org/047426m28","country_code":"US","type":"education","lineage":["https://openalex.org/I157725225"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Xin Chen","raw_affiliation_strings":["Department of Industrial and Enterprise System Engineering, University of Illinois at Urbana\u2013Champaign, Urbana, 61801, IL, USA","Department of Industrial and Enterprise System Engineering, University of Illinois at Urbana-Champaign, Urbana, USA 61801#TAB#"],"affiliations":[{"raw_affiliation_string":"Department of Industrial and Enterprise System Engineering, University of Illinois at Urbana\u2013Champaign, Urbana, 61801, IL, USA","institution_ids":["https://openalex.org/I157725225"]},{"raw_affiliation_string":"Department of Industrial and Enterprise System Engineering, University of Illinois at Urbana-Champaign, Urbana, USA 61801#TAB#","institution_ids":["https://openalex.org/I157725225"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5090153413","display_name":"Shaohua Pan","orcid":"https://orcid.org/0000-0002-6261-5268"},"institutions":[{"id":"https://openalex.org/I90610280","display_name":"South China University of Technology","ror":"https://ror.org/0530pts50","country_code":"CN","type":"education","lineage":["https://openalex.org/I90610280"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Shaohua Pan","raw_affiliation_strings":["School of Mathematical Sciences, South China University of Technology, Guangzhou, 510640, China","School of Mathematical Sciences, South China University of Technology, Guangzhou, China 510640#TAB#"],"affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences, South China University of Technology, Guangzhou, 510640, China","institution_ids":["https://openalex.org/I90610280"]},{"raw_affiliation_string":"School of Mathematical Sciences, South China University of Technology, Guangzhou, China 510640#TAB#","institution_ids":["https://openalex.org/I90610280"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100462859","display_name":"Jiawei Zhang","orcid":"https://orcid.org/0000-0003-4988-6028"},"institutions":[{"id":"https://openalex.org/I57206974","display_name":"New York University","ror":"https://ror.org/0190ak572","country_code":"US","type":"education","lineage":["https://openalex.org/I57206974"]},{"id":"https://openalex.org/I4210155590","display_name":"Management Sciences (United States)","ror":"https://ror.org/05shz5j84","country_code":"US","type":"company","lineage":["https://openalex.org/I4210155590"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Jiawei Zhang","raw_affiliation_strings":["Department of Information, Operations and Management Sciences, New York University, New York, 10012-1126, NY, USA","Department of Information, Operations and Management Sciences, New York University, New York, USA 10012-1126"],"affiliations":[{"raw_affiliation_string":"Department of Information, Operations and Management Sciences, New York University, New York, 10012-1126, NY, USA","institution_ids":["https://openalex.org/I57206974","https://openalex.org/I4210155590"]},{"raw_affiliation_string":"Department of Information, Operations and Management Sciences, New York University, New York, USA 10012-1126","institution_ids":["https://openalex.org/I57206974"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5061633817"],"corresponding_institution_ids":["https://openalex.org/I134161618"],"apc_list":{"value":2190,"currency":"EUR","value_usd":2780},"apc_paid":null,"fwci":0.5134,"has_fulltext":false,"cited_by_count":12,"citation_normalized_percentile":{"value":0.70528684,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"45","issue":"2","first_page":"259","last_page":"279"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9995999932289124,"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":0.9995999932289124,"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":0.9991999864578247,"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/T11564","display_name":"Mathematical Inequalities and Applications","score":0.9991999864578247,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/mathematics","display_name":"Mathematics","score":0.8390734195709229},{"id":"https://openalex.org/keywords/monotone-polygon","display_name":"Monotone polygon","score":0.757222056388855},{"id":"https://openalex.org/keywords/monotonic-function","display_name":"Monotonic function","score":0.638290286064148},{"id":"https://openalex.org/keywords/convex-function","display_name":"Convex function","score":0.584135890007019},{"id":"https://openalex.org/keywords/convexity","display_name":"Convexity","score":0.5791803002357483},{"id":"https://openalex.org/keywords/differentiable-function","display_name":"Differentiable function","score":0.5624905228614807},{"id":"https://openalex.org/keywords/convex-optimization","display_name":"Convex optimization","score":0.5287627577781677},{"id":"https://openalex.org/keywords/subderivative","display_name":"Subderivative","score":0.5238801836967468},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.5179821252822876},{"id":"https://openalex.org/keywords/proper-convex-function","display_name":"Proper convex function","score":0.4688226878643036},{"id":"https://openalex.org/keywords/convex-analysis","display_name":"Convex analysis","score":0.45135414600372314},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.4372304379940033},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.4109795093536377},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3716556429862976},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3520103096961975},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.2919830083847046},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.2614189684391022},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.05551663041114807}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8390734195709229},{"id":"https://openalex.org/C2834757","wikidata":"https://www.wikidata.org/wiki/Q4925424","display_name":"Monotone polygon","level":2,"score":0.757222056388855},{"id":"https://openalex.org/C72169020","wikidata":"https://www.wikidata.org/wiki/Q194404","display_name":"Monotonic function","level":2,"score":0.638290286064148},{"id":"https://openalex.org/C145446738","wikidata":"https://www.wikidata.org/wiki/Q319913","display_name":"Convex function","level":3,"score":0.584135890007019},{"id":"https://openalex.org/C72134830","wikidata":"https://www.wikidata.org/wiki/Q5166524","display_name":"Convexity","level":2,"score":0.5791803002357483},{"id":"https://openalex.org/C202615002","wikidata":"https://www.wikidata.org/wiki/Q783507","display_name":"Differentiable function","level":2,"score":0.5624905228614807},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.5287627577781677},{"id":"https://openalex.org/C200661725","wikidata":"https://www.wikidata.org/wiki/Q289500","display_name":"Subderivative","level":4,"score":0.5238801836967468},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.5179821252822876},{"id":"https://openalex.org/C50862404","wikidata":"https://www.wikidata.org/wiki/Q3075259","display_name":"Proper convex function","level":5,"score":0.4688226878643036},{"id":"https://openalex.org/C12108790","wikidata":"https://www.wikidata.org/wiki/Q2234833","display_name":"Convex analysis","level":4,"score":0.45135414600372314},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.4372304379940033},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.4109795093536377},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3716556429862976},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3520103096961975},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.2919830083847046},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2614189684391022},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.05551663041114807},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"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/C106159729","wikidata":"https://www.wikidata.org/wiki/Q2294553","display_name":"Financial economics","level":1,"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/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/s10898-008-9373-z","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10898-008-9373-z","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:CiteSeerX.psu:10.1.1.721.8687","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.721.8687","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://publish.illinois.edu/xinchen/files/2012/12/SOCconvex.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":21,"referenced_works":["https://openalex.org/W10800830","https://openalex.org/W160580173","https://openalex.org/W391578156","https://openalex.org/W1021192518","https://openalex.org/W1488435683","https://openalex.org/W1973281249","https://openalex.org/W2004596681","https://openalex.org/W2017580271","https://openalex.org/W2018695900","https://openalex.org/W2042360648","https://openalex.org/W2057795645","https://openalex.org/W2075649590","https://openalex.org/W2093461426","https://openalex.org/W2099312443","https://openalex.org/W2127930751","https://openalex.org/W2148160941","https://openalex.org/W2163964304","https://openalex.org/W2572594781","https://openalex.org/W2610857016","https://openalex.org/W2798707604","https://openalex.org/W4255333822"],"related_works":["https://openalex.org/W2007576447","https://openalex.org/W2026600343","https://openalex.org/W2356261519","https://openalex.org/W4382519084","https://openalex.org/W2478309485","https://openalex.org/W165488893","https://openalex.org/W2040676043","https://openalex.org/W1510770274","https://openalex.org/W4361807553","https://openalex.org/W2185500298"],"abstract_inverted_index":null,"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":2},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":1}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}
