{"id":"https://openalex.org/W2924133724","doi":"https://doi.org/10.1007/s10957-019-01499-7","title":"On Solving Nonsmooth Mixed-Integer Nonlinear Programming Problems by Outer Approximation and Generalized Benders Decomposition","display_name":"On Solving Nonsmooth Mixed-Integer Nonlinear Programming Problems by Outer Approximation and Generalized Benders Decomposition","publication_year":2019,"publication_date":"2019-03-19","ids":{"openalex":"https://openalex.org/W2924133724","doi":"https://doi.org/10.1007/s10957-019-01499-7","mag":"2924133724"},"language":"en","primary_location":{"id":"doi:10.1007/s10957-019-01499-7","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10957-019-01499-7","pdf_url":null,"source":{"id":"https://openalex.org/S52430896","display_name":"Journal of Optimization Theory and Applications","issn_l":"0022-3239","issn":["0022-3239","1573-2878"],"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 Optimization Theory and Applications","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/A5101749447","display_name":"Zhou Wei","orcid":"https://orcid.org/0000-0001-8895-8755"},"institutions":[{"id":"https://openalex.org/I189210763","display_name":"Yunnan University","ror":"https://ror.org/0040axw97","country_code":"CN","type":"education","lineage":["https://openalex.org/I189210763"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zhou Wei","raw_affiliation_strings":["Department of Mathematics, Yunnan University, Kunming, 650091, People\u2019s Republic of China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Yunnan University, Kunming, 650091, People\u2019s Republic of China","institution_ids":["https://openalex.org/I189210763"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5008314297","display_name":"M. Montaz Ali","orcid":"https://orcid.org/0000-0003-0864-8146"},"institutions":[{"id":"https://openalex.org/I192619145","display_name":"University of the Witwatersrand","ror":"https://ror.org/03rp50x72","country_code":"ZA","type":"education","lineage":["https://openalex.org/I192619145"]}],"countries":["ZA"],"is_corresponding":false,"raw_author_name":"M. Montaz Ali","raw_affiliation_strings":["School of Computer Science and Applied Mathematics, University of the Witwatersrand, Wits, Johannesburg, 2050, South Africa"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Computer Science and Applied Mathematics, University of the Witwatersrand, Wits, Johannesburg, 2050, South Africa","institution_ids":["https://openalex.org/I192619145"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5006523413","display_name":"Liang Xu","orcid":"https://orcid.org/0000-0003-2890-4872"},"institutions":[{"id":"https://openalex.org/I170201317","display_name":"University of Pittsburgh","ror":"https://ror.org/01an3r305","country_code":"US","type":"education","lineage":["https://openalex.org/I170201317"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Liang Xu","raw_affiliation_strings":["Department of Industrial Engineering, University of Pittsburgh, Pittsburgh, PA, 15261, USA"],"raw_orcid":"https://orcid.org/0000-0003-2890-4872","affiliations":[{"raw_affiliation_string":"Department of Industrial Engineering, University of Pittsburgh, Pittsburgh, PA, 15261, USA","institution_ids":["https://openalex.org/I170201317"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100732720","display_name":"Bo Zeng","orcid":"https://orcid.org/0000-0002-8689-4281"},"institutions":[{"id":"https://openalex.org/I170201317","display_name":"University of Pittsburgh","ror":"https://ror.org/01an3r305","country_code":"US","type":"education","lineage":["https://openalex.org/I170201317"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Bo Zeng","raw_affiliation_strings":["Department of Industrial Engineering, University of Pittsburgh, Pittsburgh, PA, 15261, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Industrial Engineering, University of Pittsburgh, Pittsburgh, PA, 15261, USA","institution_ids":["https://openalex.org/I170201317"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5050520268","display_name":"Jen\u2010Chih Yao","orcid":"https://orcid.org/0000-0001-9041-3375"},"institutions":[{"id":"https://openalex.org/I135237710","display_name":"Zhejiang Normal University","ror":"https://ror.org/01vevwk45","country_code":"CN","type":"education","lineage":["https://openalex.org/I135237710"]},{"id":"https://openalex.org/I184693016","display_name":"China Medical University","ror":"https://ror.org/00v408z34","country_code":"TW","type":"education","lineage":["https://openalex.org/I184693016"]},{"id":"https://openalex.org/I4210126829","display_name":"China Medical University Hospital","ror":"https://ror.org/0368s4g32","country_code":"TW","type":"healthcare","lineage":["https://openalex.org/I4210126829"]}],"countries":["CN","TW"],"is_corresponding":true,"raw_author_name":"Jen-Chih Yao","raw_affiliation_strings":["Department of Mathematics, Zhejiang Normal University, Jinhua, 321004, People\u2019s Republic of China","Research Center for Interneural Computing, China Medical University Hospital, China Medical University, Taichung, 40402, Taiwan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Zhejiang Normal University, Jinhua, 321004, People\u2019s Republic of China","institution_ids":["https://openalex.org/I135237710"]},{"raw_affiliation_string":"Research Center for Interneural Computing, China Medical University Hospital, China Medical University, Taichung, 40402, Taiwan","institution_ids":["https://openalex.org/I4210126829","https://openalex.org/I184693016"]}]}],"institutions":[],"countries_distinct_count":4,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5050520268"],"corresponding_institution_ids":["https://openalex.org/I135237710","https://openalex.org/I184693016","https://openalex.org/I4210126829"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":null,"fwci":1.2978,"has_fulltext":false,"cited_by_count":8,"citation_normalized_percentile":{"value":0.77460902,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"181","issue":"3","first_page":"840","last_page":"863"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9997000098228455,"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":0.9997000098228455,"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":0.9993000030517578,"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/T12709","display_name":"Optimization and Mathematical Programming","score":0.9984999895095825,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"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":0.7942676544189453},{"id":"https://openalex.org/keywords/benders-decomposition","display_name":"Benders' decomposition","score":0.7298049330711365},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.607296347618103},{"id":"https://openalex.org/keywords/conic-section","display_name":"Conic section","score":0.6018282771110535},{"id":"https://openalex.org/keywords/theory-of-computation","display_name":"Theory of computation","score":0.5745956897735596},{"id":"https://openalex.org/keywords/differentiable-function","display_name":"Differentiable function","score":0.5721548795700073},{"id":"https://openalex.org/keywords/nonlinear-programming","display_name":"Nonlinear programming","score":0.525965690612793},{"id":"https://openalex.org/keywords/decomposition","display_name":"Decomposition","score":0.4950496256351471},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.45054471492767334},{"id":"https://openalex.org/keywords/decomposition-method","display_name":"Decomposition method (queueing theory)","score":0.4488181173801422},{"id":"https://openalex.org/keywords/integer","display_name":"Integer (computer science)","score":0.4367109537124634},{"id":"https://openalex.org/keywords/integer-programming","display_name":"Integer programming","score":0.4254623353481293},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.42129838466644287},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.24734652042388916},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.16995149850845337},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.16241323947906494},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.13144168257713318},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.06110149621963501}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7942676544189453},{"id":"https://openalex.org/C27665512","wikidata":"https://www.wikidata.org/wiki/Q3042795","display_name":"Benders' decomposition","level":2,"score":0.7298049330711365},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.607296347618103},{"id":"https://openalex.org/C108598597","wikidata":"https://www.wikidata.org/wiki/Q124255","display_name":"Conic section","level":2,"score":0.6018282771110535},{"id":"https://openalex.org/C24858836","wikidata":"https://www.wikidata.org/wiki/Q844718","display_name":"Theory of computation","level":2,"score":0.5745956897735596},{"id":"https://openalex.org/C202615002","wikidata":"https://www.wikidata.org/wiki/Q783507","display_name":"Differentiable function","level":2,"score":0.5721548795700073},{"id":"https://openalex.org/C115527620","wikidata":"https://www.wikidata.org/wiki/Q769909","display_name":"Nonlinear programming","level":3,"score":0.525965690612793},{"id":"https://openalex.org/C124681953","wikidata":"https://www.wikidata.org/wiki/Q339062","display_name":"Decomposition","level":2,"score":0.4950496256351471},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.45054471492767334},{"id":"https://openalex.org/C2778258933","wikidata":"https://www.wikidata.org/wiki/Q16918986","display_name":"Decomposition method (queueing theory)","level":2,"score":0.4488181173801422},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.4367109537124634},{"id":"https://openalex.org/C56086750","wikidata":"https://www.wikidata.org/wiki/Q6042592","display_name":"Integer programming","level":2,"score":0.4254623353481293},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.42129838466644287},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.24734652042388916},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.16995149850845337},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.16241323947906494},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.13144168257713318},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.06110149621963501},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","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/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/s10957-019-01499-7","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10957-019-01499-7","pdf_url":null,"source":{"id":"https://openalex.org/S52430896","display_name":"Journal of Optimization Theory and Applications","issn_l":"0022-3239","issn":["0022-3239","1573-2878"],"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 Optimization Theory and Applications","raw_type":"journal-article"},{"id":"pmh:oai:RePEc:spr:joptap:v:181:y:2019:i:3:d:10.1007_s10957-019-01499-7","is_oa":false,"landing_page_url":"http://link.springer.com/10.1007/s10957-019-01499-7","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":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":32,"referenced_works":["https://openalex.org/W10227180","https://openalex.org/W114465074","https://openalex.org/W181437557","https://openalex.org/W1492700492","https://openalex.org/W1508945008","https://openalex.org/W1541170979","https://openalex.org/W1563600186","https://openalex.org/W1667969928","https://openalex.org/W1970544310","https://openalex.org/W1997215277","https://openalex.org/W2004407575","https://openalex.org/W2007231110","https://openalex.org/W2044121814","https://openalex.org/W2049256228","https://openalex.org/W2057338659","https://openalex.org/W2061962896","https://openalex.org/W2069402544","https://openalex.org/W2069808690","https://openalex.org/W2071334094","https://openalex.org/W2072004299","https://openalex.org/W2088836601","https://openalex.org/W2090633148","https://openalex.org/W2114605231","https://openalex.org/W2117160627","https://openalex.org/W2135588736","https://openalex.org/W2166797227","https://openalex.org/W2169427658","https://openalex.org/W2170213261","https://openalex.org/W2219010958","https://openalex.org/W3104448045","https://openalex.org/W4285719527","https://openalex.org/W4302408205"],"related_works":["https://openalex.org/W1993356786","https://openalex.org/W2012045681","https://openalex.org/W2088344732","https://openalex.org/W2064698314","https://openalex.org/W4236859340","https://openalex.org/W2462476910","https://openalex.org/W4384009877","https://openalex.org/W2089185195","https://openalex.org/W4220674099","https://openalex.org/W1999365111"],"abstract_inverted_index":null,"counts_by_year":[{"year":2025,"cited_by_count":3},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}