{"id":"https://openalex.org/W4244248310","doi":"https://doi.org/10.1504/ijmor.2016.10000149","title":"Symmetric duality in non-differentiable programming using G-invexity","display_name":"Symmetric duality in non-differentiable programming using G-invexity","publication_year":2016,"publication_date":"2016-01-01","ids":{"openalex":"https://openalex.org/W4244248310","doi":"https://doi.org/10.1504/ijmor.2016.10000149"},"language":"en","primary_location":{"id":"doi:10.1504/ijmor.2016.10000149","is_oa":false,"landing_page_url":"https://doi.org/10.1504/ijmor.2016.10000149","pdf_url":null,"source":{"id":"https://openalex.org/S135796719","display_name":"International Journal of Mathematics in Operational Research","issn_l":"1757-5850","issn":["1757-5850","1757-5869"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310317825","host_organization_name":"Inderscience Publishers","host_organization_lineage":["https://openalex.org/P4310317825"],"host_organization_lineage_names":["Inderscience Publishers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Mathematics in 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/A5079725730","display_name":"Ramu Dubey","orcid":"https://orcid.org/0000-0001-8434-0907"},"institutions":[{"id":"https://openalex.org/I154851008","display_name":"Indian Institute of Technology Roorkee","ror":"https://ror.org/00582g326","country_code":"IN","type":"education","lineage":["https://openalex.org/I154851008"]}],"countries":["IN"],"is_corresponding":true,"raw_author_name":"Ramu Dubey","raw_affiliation_strings":["Department of Mathematics, Indian Institute of Technology Roorkee, Roorkee-247667, India"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Indian Institute of Technology Roorkee, Roorkee-247667, India","institution_ids":["https://openalex.org/I154851008"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5101702201","display_name":"Shivam Gupta","orcid":"https://orcid.org/0000-0002-2084-1128"},"institutions":[{"id":"https://openalex.org/I154851008","display_name":"Indian Institute of Technology Roorkee","ror":"https://ror.org/00582g326","country_code":"IN","type":"education","lineage":["https://openalex.org/I154851008"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"S.K. Gupta","raw_affiliation_strings":["Department of Mathematics, Indian Institute of Technology Roorkee, Roorkee-247667, India"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Indian Institute of Technology Roorkee, Roorkee-247667, India","institution_ids":["https://openalex.org/I154851008"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5079725730"],"corresponding_institution_ids":["https://openalex.org/I154851008"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.24203367,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"9","issue":"3","first_page":"395","last_page":"395"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10545","display_name":"Optimization and Variational Analysis","score":0.9973999857902527,"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":0.9973999857902527,"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":0.9764999747276306,"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"}},{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9146000146865845,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/differentiable-function","display_name":"Differentiable function","score":0.7999404668807983},{"id":"https://openalex.org/keywords/duality","display_name":"Duality (order theory)","score":0.7730401754379272},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6289635300636292},{"id":"https://openalex.org/keywords/converse","display_name":"Converse","score":0.6270921230316162},{"id":"https://openalex.org/keywords/duality-gap","display_name":"Duality gap","score":0.5423094034194946},{"id":"https://openalex.org/keywords/wolfe-duality","display_name":"Wolfe duality","score":0.538201093673706},{"id":"https://openalex.org/keywords/convexity","display_name":"Convexity","score":0.47790154814720154},{"id":"https://openalex.org/keywords/strong-duality","display_name":"Strong duality","score":0.425086110830307},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.39246463775634766},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3614107668399811},{"id":"https://openalex.org/keywords/weak-duality","display_name":"Weak duality","score":0.3523269295692444},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.2736033797264099},{"id":"https://openalex.org/keywords/optimization-problem","display_name":"Optimization problem","score":0.16431376338005066},{"id":"https://openalex.org/keywords/finance","display_name":"Finance","score":0.05953037738800049},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.04980143904685974}],"concepts":[{"id":"https://openalex.org/C202615002","wikidata":"https://www.wikidata.org/wiki/Q783507","display_name":"Differentiable function","level":2,"score":0.7999404668807983},{"id":"https://openalex.org/C2778023678","wikidata":"https://www.wikidata.org/wiki/Q554403","display_name":"Duality (order theory)","level":2,"score":0.7730401754379272},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6289635300636292},{"id":"https://openalex.org/C2776809875","wikidata":"https://www.wikidata.org/wiki/Q1375963","display_name":"Converse","level":2,"score":0.6270921230316162},{"id":"https://openalex.org/C5274546","wikidata":"https://www.wikidata.org/wiki/Q5310264","display_name":"Duality gap","level":3,"score":0.5423094034194946},{"id":"https://openalex.org/C109456813","wikidata":"https://www.wikidata.org/wiki/Q8029991","display_name":"Wolfe duality","level":5,"score":0.538201093673706},{"id":"https://openalex.org/C72134830","wikidata":"https://www.wikidata.org/wiki/Q5166524","display_name":"Convexity","level":2,"score":0.47790154814720154},{"id":"https://openalex.org/C163863214","wikidata":"https://www.wikidata.org/wiki/Q7624553","display_name":"Strong duality","level":3,"score":0.425086110830307},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.39246463775634766},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3614107668399811},{"id":"https://openalex.org/C80682859","wikidata":"https://www.wikidata.org/wiki/Q7977943","display_name":"Weak duality","level":4,"score":0.3523269295692444},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.2736033797264099},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.16431376338005066},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.05953037738800049},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.04980143904685974},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1504/ijmor.2016.10000149","is_oa":false,"landing_page_url":"https://doi.org/10.1504/ijmor.2016.10000149","pdf_url":null,"source":{"id":"https://openalex.org/S135796719","display_name":"International Journal of Mathematics in Operational Research","issn_l":"1757-5850","issn":["1757-5850","1757-5869"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310317825","host_organization_name":"Inderscience Publishers","host_organization_lineage":["https://openalex.org/P4310317825"],"host_organization_lineage_names":["Inderscience Publishers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Mathematics in Operational Research","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W4220928172","https://openalex.org/W3213165575","https://openalex.org/W2029896594","https://openalex.org/W2384039353","https://openalex.org/W4210245775","https://openalex.org/W2056178476","https://openalex.org/W2345066843","https://openalex.org/W1994149084","https://openalex.org/W3023033861","https://openalex.org/W2345651439"],"abstract_inverted_index":{"Mond-Weir":[0],"and":[1,6,30],"Wolfe":[2],"type":[3],"non-differentiable":[4,37],"primal":[5],"dual":[7],"symmetric":[8,38,46],"problems":[9,48],"in":[10,59],"mathematical":[11],"programming":[12,39,47],"are":[13],"formulated.":[14],"In":[15],"this":[16],"paper,":[17],"we":[18],"use":[19],"a":[20],"generalisation":[21],"of":[22,55],"convexity,":[23],"namely":[24],"G-invexity,":[25],"to":[26,51],"prove":[27],"weak,":[28],"strong":[29],"converse":[31],"duality":[32],"relations":[33],"for":[34,45],"the":[35,56,60],"two":[36],"problems.":[40],"Some":[41],"previous":[42],"known":[43],"results":[44,57],"turn":[49],"out":[50],"be":[52],"special":[53],"cases":[54],"established":[58],"paper.":[61]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
