{"id":"https://openalex.org/W4317662033","doi":"https://doi.org/10.1142/s0217595922500415","title":"On Second-Order Semi-Differentiability of Index \u03b3 of Perturbation Maps in Parametric Vector Optimization Problems","display_name":"On Second-Order Semi-Differentiability of Index \u03b3 of Perturbation Maps in Parametric Vector Optimization Problems","publication_year":2023,"publication_date":"2023-01-21","ids":{"openalex":"https://openalex.org/W4317662033","doi":"https://doi.org/10.1142/s0217595922500415"},"language":"en","primary_location":{"id":"doi:10.1142/s0217595922500415","is_oa":false,"landing_page_url":"http://dx.doi.org/10.1142/s0217595922500415","pdf_url":null,"source":{"id":"https://openalex.org/S1254427","display_name":"Asia Pacific Journal of Operational Research","issn_l":"0217-5959","issn":["0217-5959","1793-7019"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Asia-Pacific Journal of Operational Research","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/A5037171507","display_name":"Thanh-Hung Pham","orcid":"https://orcid.org/0000-0001-6839-709X"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Thanh-Hung Pham","raw_affiliation_strings":["Faculty of Pedagogy and Faculty of Social Sciences & Humanities, Kien Giang University, Chau Thanh, Kien Giang, Vietnam"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Faculty of Pedagogy and Faculty of Social Sciences & Humanities, Kien Giang University, Chau Thanh, Kien Giang, Vietnam","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5037171507"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.5315,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.55415819,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"40","issue":"06","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12396","display_name":"Advanced Differential Equations and Dynamical Systems","score":0.9937999844551086,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"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/T12396","display_name":"Advanced Differential Equations and Dynamical Systems","score":0.9937999844551086,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"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/T12727","display_name":"Differential Equations and Numerical Methods","score":0.9843000173568726,"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":0.9629999995231628,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/differentiable-function","display_name":"Differentiable function","score":0.8759678602218628},{"id":"https://openalex.org/keywords/parametric-statistics","display_name":"Parametric statistics","score":0.6892858147621155},{"id":"https://openalex.org/keywords/perturbation","display_name":"Perturbation (astronomy)","score":0.6730890274047852},{"id":"https://openalex.org/keywords/vector-optimization","display_name":"Vector optimization","score":0.5801323056221008},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5692704916000366},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5437738299369812},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.45436882972717285},{"id":"https://openalex.org/keywords/index","display_name":"Index (typography)","score":0.44648128747940063},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.4415387213230133},{"id":"https://openalex.org/keywords/optimization-problem","display_name":"Optimization problem","score":0.4126646816730499},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3164728581905365},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.29183298349380493},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.09982004761695862},{"id":"https://openalex.org/keywords/economics","display_name":"Economics","score":0.05719384551048279}],"concepts":[{"id":"https://openalex.org/C202615002","wikidata":"https://www.wikidata.org/wiki/Q783507","display_name":"Differentiable function","level":2,"score":0.8759678602218628},{"id":"https://openalex.org/C117251300","wikidata":"https://www.wikidata.org/wiki/Q1849855","display_name":"Parametric statistics","level":2,"score":0.6892858147621155},{"id":"https://openalex.org/C177918212","wikidata":"https://www.wikidata.org/wiki/Q803623","display_name":"Perturbation (astronomy)","level":2,"score":0.6730890274047852},{"id":"https://openalex.org/C164088818","wikidata":"https://www.wikidata.org/wiki/Q7917833","display_name":"Vector optimization","level":4,"score":0.5801323056221008},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5692704916000366},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5437738299369812},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.45436882972717285},{"id":"https://openalex.org/C2777382242","wikidata":"https://www.wikidata.org/wiki/Q6017816","display_name":"Index (typography)","level":2,"score":0.44648128747940063},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.4415387213230133},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.4126646816730499},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3164728581905365},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.29183298349380493},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.09982004761695862},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.05719384551048279},{"id":"https://openalex.org/C122357587","wikidata":"https://www.wikidata.org/wiki/Q6934508","display_name":"Multi-swarm optimization","level":3,"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/C136764020","wikidata":"https://www.wikidata.org/wiki/Q466","display_name":"World Wide Web","level":1,"score":0.0},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1142/s0217595922500415","is_oa":false,"landing_page_url":"http://dx.doi.org/10.1142/s0217595922500415","pdf_url":null,"source":{"id":"https://openalex.org/S1254427","display_name":"Asia Pacific Journal of Operational Research","issn_l":"0217-5959","issn":["0217-5959","1793-7019"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Asia-Pacific Journal of Operational Research","raw_type":"journal-article"},{"id":"pmh:oai:RePEc:wsi:apjorx:v:40:y:2023:i:06:n:s0217595922500415","is_oa":false,"landing_page_url":"http://www.worldscientific.com/doi/abs/10.1142/S0217595922500415","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":[{"score":0.4399999976158142,"display_name":"Climate action","id":"https://metadata.un.org/sdg/13"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":22,"referenced_works":["https://openalex.org/W34431499","https://openalex.org/W1601741115","https://openalex.org/W1884296468","https://openalex.org/W1991171386","https://openalex.org/W2002894912","https://openalex.org/W2010524577","https://openalex.org/W2011995039","https://openalex.org/W2013729684","https://openalex.org/W2013807755","https://openalex.org/W2033560262","https://openalex.org/W2037767943","https://openalex.org/W2153562582","https://openalex.org/W2478963760","https://openalex.org/W2577157308","https://openalex.org/W2801192947","https://openalex.org/W2885473730","https://openalex.org/W2951400866","https://openalex.org/W3027366238","https://openalex.org/W3039887241","https://openalex.org/W3042568622","https://openalex.org/W3157341860","https://openalex.org/W4234068421"],"related_works":["https://openalex.org/W2565276936","https://openalex.org/W2766340440","https://openalex.org/W4385713703","https://openalex.org/W109016340","https://openalex.org/W188711498","https://openalex.org/W2390455111","https://openalex.org/W3199277564","https://openalex.org/W2184300223","https://openalex.org/W2146329574","https://openalex.org/W3166454929"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"we":[3],"prove":[4],"that":[5],"the":[6,14,46],"Henig":[7,15],"global":[8,16],"proper":[9,17],"efficient":[10,18],"solution":[11],"map":[12,20],"and":[13],"perturbation":[19],"of":[21],"a":[22],"parametric":[23],"vector":[24],"optimization":[25],"problem":[26],"are":[27,42],"second-order":[28],"semi-differentiable":[29],"with":[30],"index":[31],"[Formula:":[32],"see":[33],"text]":[34],"under":[35],"some":[36],"suitable":[37],"qualification":[38],"conditions.":[39],"Several":[40],"examples":[41],"given":[43],"to":[44],"illustrate":[45],"obtained":[47],"results.":[48]},"counts_by_year":[{"year":2023,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}