{"id":"https://openalex.org/W2037160425","doi":"https://doi.org/10.1016/j.camwa.2010.09.013","title":"Saddle points criteria in nondifferentiable multiobjective programming with V -invex functions via an \u03b7 -approximation method","display_name":"Saddle points criteria in nondifferentiable multiobjective programming with V -invex functions via an \u03b7 -approximation method","publication_year":2010,"publication_date":"2010-10-04","ids":{"openalex":"https://openalex.org/W2037160425","doi":"https://doi.org/10.1016/j.camwa.2010.09.013","mag":"2037160425"},"language":"en","primary_location":{"id":"doi:10.1016/j.camwa.2010.09.013","is_oa":true,"landing_page_url":"https://doi.org/10.1016/j.camwa.2010.09.013","pdf_url":"https://www.sciencedirect.com/science/article/pii/S0898122110006991/pdf","source":{"id":"https://openalex.org/S4210205691","display_name":"Computers & Mathematics with Applications","issn_l":"0898-1221","issn":["0898-1221","1873-7668"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computers & Mathematics with Applications","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://www.sciencedirect.com/science/article/pii/S0898122110006991/pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5050602810","display_name":"Tadeusz Antczak","orcid":"https://orcid.org/0000-0002-2218-7668"},"institutions":[{"id":"https://openalex.org/I34250744","display_name":"University of \u0141\u00f3d\u017a","ror":"https://ror.org/05cq64r17","country_code":"PL","type":"education","lineage":["https://openalex.org/I34250744"]}],"countries":["PL"],"is_corresponding":true,"raw_author_name":"Tadeusz Antczak","raw_affiliation_strings":["Faculty of Mathematics and Computer Science, University of \u0141\u00f3d\u017a, Banacha 22, 90-238 \u0141\u00f3d\u017a, Poland"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Faculty of Mathematics and Computer Science, University of \u0141\u00f3d\u017a, Banacha 22, 90-238 \u0141\u00f3d\u017a, Poland","institution_ids":["https://openalex.org/I34250744"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5050602810"],"corresponding_institution_ids":["https://openalex.org/I34250744"],"apc_list":{"value":3170,"currency":"USD","value_usd":3170},"apc_paid":null,"fwci":0.3209,"has_fulltext":true,"cited_by_count":6,"citation_normalized_percentile":{"value":0.61419253,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"60","issue":"9","first_page":"2689","last_page":"2700"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10545","display_name":"Optimization and Variational Analysis","score":0.9998999834060669,"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"}},"topics":[{"id":"https://openalex.org/T10545","display_name":"Optimization and Variational Analysis","score":0.9998999834060669,"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":0.9746999740600586,"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/T12709","display_name":"Optimization and Mathematical Programming","score":0.9624999761581421,"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":0.7559353113174438},{"id":"https://openalex.org/keywords/saddle-point","display_name":"Saddle point","score":0.6018924713134766},{"id":"https://openalex.org/keywords/pareto-principle","display_name":"Pareto principle","score":0.5364867448806763},{"id":"https://openalex.org/keywords/saddle","display_name":"Saddle","score":0.534263014793396},{"id":"https://openalex.org/keywords/multi-objective-optimization","display_name":"Multi-objective optimization","score":0.5246931910514832},{"id":"https://openalex.org/keywords/lagrange-multiplier","display_name":"Lagrange multiplier","score":0.48076340556144714},{"id":"https://openalex.org/keywords/equivalence","display_name":"Equivalence (formal languages)","score":0.4777885377407074},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.4661814868450165},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.38112419843673706},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.36975589394569397},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3258844017982483},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.08864098787307739}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7559353113174438},{"id":"https://openalex.org/C2681867","wikidata":"https://www.wikidata.org/wiki/Q690935","display_name":"Saddle point","level":2,"score":0.6018924713134766},{"id":"https://openalex.org/C137635306","wikidata":"https://www.wikidata.org/wiki/Q182667","display_name":"Pareto principle","level":2,"score":0.5364867448806763},{"id":"https://openalex.org/C2777127463","wikidata":"https://www.wikidata.org/wiki/Q10862618","display_name":"Saddle","level":2,"score":0.534263014793396},{"id":"https://openalex.org/C68781425","wikidata":"https://www.wikidata.org/wiki/Q2052203","display_name":"Multi-objective optimization","level":2,"score":0.5246931910514832},{"id":"https://openalex.org/C73684929","wikidata":"https://www.wikidata.org/wiki/Q598870","display_name":"Lagrange multiplier","level":2,"score":0.48076340556144714},{"id":"https://openalex.org/C2780069185","wikidata":"https://www.wikidata.org/wiki/Q7977945","display_name":"Equivalence (formal languages)","level":2,"score":0.4777885377407074},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4661814868450165},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.38112419843673706},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.36975589394569397},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3258844017982483},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.08864098787307739}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1016/j.camwa.2010.09.013","is_oa":true,"landing_page_url":"https://doi.org/10.1016/j.camwa.2010.09.013","pdf_url":"https://www.sciencedirect.com/science/article/pii/S0898122110006991/pdf","source":{"id":"https://openalex.org/S4210205691","display_name":"Computers & Mathematics with Applications","issn_l":"0898-1221","issn":["0898-1221","1873-7668"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computers & Mathematics with Applications","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1016/j.camwa.2010.09.013","is_oa":true,"landing_page_url":"https://doi.org/10.1016/j.camwa.2010.09.013","pdf_url":"https://www.sciencedirect.com/science/article/pii/S0898122110006991/pdf","source":{"id":"https://openalex.org/S4210205691","display_name":"Computers & Mathematics with Applications","issn_l":"0898-1221","issn":["0898-1221","1873-7668"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computers & Mathematics with Applications","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2037160425.pdf","grobid_xml":"https://content.openalex.org/works/W2037160425.grobid-xml"},"referenced_works_count":29,"referenced_works":["https://openalex.org/W25288802","https://openalex.org/W55781765","https://openalex.org/W205965983","https://openalex.org/W1538305605","https://openalex.org/W1974326837","https://openalex.org/W1974958764","https://openalex.org/W1977310087","https://openalex.org/W1985164244","https://openalex.org/W2001348424","https://openalex.org/W2007079240","https://openalex.org/W2011495370","https://openalex.org/W2014939542","https://openalex.org/W2020867778","https://openalex.org/W2051000168","https://openalex.org/W2073956415","https://openalex.org/W2093920465","https://openalex.org/W2094786643","https://openalex.org/W2095172861","https://openalex.org/W2111857415","https://openalex.org/W2123439314","https://openalex.org/W2313488898","https://openalex.org/W2330538100","https://openalex.org/W2548487998","https://openalex.org/W4238366554","https://openalex.org/W6602284407","https://openalex.org/W6608417898","https://openalex.org/W6632041090","https://openalex.org/W6655520665","https://openalex.org/W6663193378"],"related_works":["https://openalex.org/W4236459141","https://openalex.org/W4205304778","https://openalex.org/W2020252434","https://openalex.org/W3127021889","https://openalex.org/W73248859","https://openalex.org/W2584253892","https://openalex.org/W4308799551","https://openalex.org/W2350324449","https://openalex.org/W119381072","https://openalex.org/W2034033896"],"abstract_inverted_index":null,"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":2},{"year":2021,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2013,"cited_by_count":1}],"updated_date":"2026-08-21T09:56:20.448147","created_date":"2025-10-10T00:00:00"}