{"id":"https://openalex.org/W1990787369","doi":"https://doi.org/10.2478/v10006-011-0024-z","title":"Random perturbation of the projected variable metric method for nonsmooth nonconvex optimization problems with linear constraints","display_name":"Random perturbation of the projected variable metric method for nonsmooth nonconvex optimization problems with linear constraints","publication_year":2011,"publication_date":"2011-06-01","ids":{"openalex":"https://openalex.org/W1990787369","doi":"https://doi.org/10.2478/v10006-011-0024-z","mag":"1990787369"},"language":"en","primary_location":{"id":"doi:10.2478/v10006-011-0024-z","is_oa":true,"landing_page_url":"https://doi.org/10.2478/v10006-011-0024-z","pdf_url":"https://sciendo.com/pdf/10.2478/v10006-011-0024-z","source":{"id":"https://openalex.org/S117679522","display_name":"International Journal of Applied Mathematics and Computer Science","issn_l":"1641-876X","issn":["1641-876X","2083-8492"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310320322","host_organization_name":"De Gruyter Open","host_organization_lineage":["https://openalex.org/P4310320322","https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter Open","De Gruyter"],"type":"journal"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Applied Mathematics and Computer Science","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://sciendo.com/pdf/10.2478/v10006-011-0024-z","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5089447839","display_name":"Abdelkrim El Mouatasim","orcid":"https://orcid.org/0000-0001-9947-1408"},"institutions":[{"id":"https://openalex.org/I91450128","display_name":"Jazan University","ror":"https://ror.org/02bjnq803","country_code":"SA","type":"education","lineage":["https://openalex.org/I91450128"]}],"countries":["SA"],"is_corresponding":true,"raw_author_name":"Abdelkrim El Mouatasim","raw_affiliation_strings":["Department of Mathematics, Faculty of Science, Jazan University, P.B. 2097, Jazan, Saudi Arabia"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Faculty of Science, Jazan University, P.B. 2097, Jazan, Saudi Arabia","institution_ids":["https://openalex.org/I91450128"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5083730212","display_name":"Rachid Ellaia","orcid":null},"institutions":[{"id":"https://openalex.org/I126477371","display_name":"Mohammed V University","ror":"https://ror.org/00r8w8f84","country_code":"MA","type":"education","lineage":["https://openalex.org/I126477371"]},{"id":"https://openalex.org/I127336678","display_name":"Ecole Mohammadia d'Ing\u00e9nieurs","ror":"https://ror.org/00md3qm14","country_code":"MA","type":"education","lineage":["https://openalex.org/I127336678"]}],"countries":["MA"],"is_corresponding":false,"raw_author_name":"Rachid Ellaia","raw_affiliation_strings":["Laboratory of Study and Research in Applied Mathematics, Mohammadia School of Engineers, Mohammed V Agdal University, Ab Ibn sina, BP 765, Agdal, Rabat, Morocco#TAB#"],"affiliations":[{"raw_affiliation_string":"Laboratory of Study and Research in Applied Mathematics, Mohammadia School of Engineers, Mohammed V Agdal University, Ab Ibn sina, BP 765, Agdal, Rabat, Morocco#TAB#","institution_ids":["https://openalex.org/I126477371","https://openalex.org/I127336678"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5007518223","display_name":"Eduardo Souza de Cursi","orcid":"https://orcid.org/0000-0001-9184-2489"},"institutions":[{"id":"https://openalex.org/I196454796","display_name":"Institut National des Sciences Appliqu\u00e9es de Toulouse","ror":"https://ror.org/01h8pf755","country_code":"FR","type":"education","lineage":["https://openalex.org/I196454796","https://openalex.org/I4405258862"]},{"id":"https://openalex.org/I88814501","display_name":"Institut National des Sciences Appliqu\u00e9es Rouen Normandie","ror":"https://ror.org/020ws7586","country_code":"FR","type":"education","lineage":["https://openalex.org/I4210105918","https://openalex.org/I88814501"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Eduardo de Cursi","raw_affiliation_strings":["National Institute for Applied Sciences, Rouen Avenue de l'Universit\u00e9, BP 8, Saint-Etienne du Rouvray, France#TAB#"],"affiliations":[{"raw_affiliation_string":"National Institute for Applied Sciences, Rouen Avenue de l'Universit\u00e9, BP 8, Saint-Etienne du Rouvray, France#TAB#","institution_ids":["https://openalex.org/I88814501","https://openalex.org/I196454796"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5089447839"],"corresponding_institution_ids":["https://openalex.org/I91450128"],"apc_list":{"value":4080,"currency":"PLN","value_usd":1100},"apc_paid":{"value":4080,"currency":"PLN","value_usd":1100},"fwci":0.3231,"has_fulltext":true,"cited_by_count":6,"citation_normalized_percentile":{"value":0.58595465,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"21","issue":"2","first_page":"317","last_page":"329"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10545","display_name":"Optimization and Variational Analysis","score":0.9994000196456909,"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":0.9994000196456909,"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":0.9984999895095825,"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/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9932000041007996,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"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/lipschitz-continuity","display_name":"Lipschitz continuity","score":0.8171448111534119},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7804584503173828},{"id":"https://openalex.org/keywords/perturbation","display_name":"Perturbation (astronomy)","score":0.6723138093948364},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5653992891311646},{"id":"https://openalex.org/keywords/optimization-problem","display_name":"Optimization problem","score":0.5218583345413208},{"id":"https://openalex.org/keywords/feasible-region","display_name":"Feasible region","score":0.512316107749939},{"id":"https://openalex.org/keywords/countable-set","display_name":"Countable set","score":0.4965096116065979},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.4702680706977844},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4539690613746643},{"id":"https://openalex.org/keywords/metric","display_name":"Metric (unit)","score":0.4523979425430298},{"id":"https://openalex.org/keywords/random-variable","display_name":"Random variable","score":0.43969565629959106},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.16380459070205688},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.07808682322502136}],"concepts":[{"id":"https://openalex.org/C22324862","wikidata":"https://www.wikidata.org/wiki/Q652707","display_name":"Lipschitz continuity","level":2,"score":0.8171448111534119},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7804584503173828},{"id":"https://openalex.org/C177918212","wikidata":"https://www.wikidata.org/wiki/Q803623","display_name":"Perturbation (astronomy)","level":2,"score":0.6723138093948364},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5653992891311646},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.5218583345413208},{"id":"https://openalex.org/C177067428","wikidata":"https://www.wikidata.org/wiki/Q17013331","display_name":"Feasible region","level":2,"score":0.512316107749939},{"id":"https://openalex.org/C110729354","wikidata":"https://www.wikidata.org/wiki/Q185478","display_name":"Countable set","level":2,"score":0.4965096116065979},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.4702680706977844},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4539690613746643},{"id":"https://openalex.org/C176217482","wikidata":"https://www.wikidata.org/wiki/Q860554","display_name":"Metric (unit)","level":2,"score":0.4523979425430298},{"id":"https://openalex.org/C122123141","wikidata":"https://www.wikidata.org/wiki/Q176623","display_name":"Random variable","level":2,"score":0.43969565629959106},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.16380459070205688},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.07808682322502136},{"id":"https://openalex.org/C21547014","wikidata":"https://www.wikidata.org/wiki/Q1423657","display_name":"Operations management","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},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.2478/v10006-011-0024-z","is_oa":true,"landing_page_url":"https://doi.org/10.2478/v10006-011-0024-z","pdf_url":"https://sciendo.com/pdf/10.2478/v10006-011-0024-z","source":{"id":"https://openalex.org/S117679522","display_name":"International Journal of Applied Mathematics and Computer Science","issn_l":"1641-876X","issn":["1641-876X","2083-8492"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310320322","host_organization_name":"De Gruyter Open","host_organization_lineage":["https://openalex.org/P4310320322","https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter Open","De Gruyter"],"type":"journal"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Applied Mathematics and Computer Science","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.390.6658","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.390.6658","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://matwbn.icm.edu.pl/ksiazki/amc/amc21/amc2129.pdf","raw_type":"text"},{"id":"pmh:oai:zbc.uz.zgora.pl:46919","is_oa":false,"landing_page_url":"https://zbc.uz.zgora.pl/dlibra/docmetadata?showContent=true&id=46919","pdf_url":null,"source":{"id":"https://openalex.org/S4306400400","display_name":"Digital library of Zielona Gora (University of Zielona G\u00f3ra)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I46305939","host_organization_name":"University of Zielona G\u00f3ra","host_organization_lineage":["https://openalex.org/I46305939"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"https://www.amcs.uz.zgora.pl/?action=paper&paper=554","raw_type":"artyku\u0142"}],"best_oa_location":{"id":"doi:10.2478/v10006-011-0024-z","is_oa":true,"landing_page_url":"https://doi.org/10.2478/v10006-011-0024-z","pdf_url":"https://sciendo.com/pdf/10.2478/v10006-011-0024-z","source":{"id":"https://openalex.org/S117679522","display_name":"International Journal of Applied Mathematics and Computer Science","issn_l":"1641-876X","issn":["1641-876X","2083-8492"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310320322","host_organization_name":"De Gruyter Open","host_organization_lineage":["https://openalex.org/P4310320322","https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter Open","De Gruyter"],"type":"journal"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Applied Mathematics and Computer Science","raw_type":"journal-article"},"sustainable_development_goals":[{"display_name":"Reduced inequalities","score":0.4300000071525574,"id":"https://metadata.un.org/sdg/10"}],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1990787369.pdf","grobid_xml":"https://content.openalex.org/works/W1990787369.grobid-xml"},"referenced_works_count":42,"referenced_works":["https://openalex.org/W90226210","https://openalex.org/W266914838","https://openalex.org/W581935970","https://openalex.org/W1519482519","https://openalex.org/W1521386166","https://openalex.org/W1540276704","https://openalex.org/W1553702074","https://openalex.org/W1590061462","https://openalex.org/W1645039792","https://openalex.org/W1964755931","https://openalex.org/W1971290991","https://openalex.org/W1971620831","https://openalex.org/W2005136695","https://openalex.org/W2013226802","https://openalex.org/W2022772618","https://openalex.org/W2030912188","https://openalex.org/W2038210983","https://openalex.org/W2041928877","https://openalex.org/W2042803051","https://openalex.org/W2056641273","https://openalex.org/W2067375490","https://openalex.org/W2069808690","https://openalex.org/W2071609006","https://openalex.org/W2078409719","https://openalex.org/W2080103296","https://openalex.org/W2083432309","https://openalex.org/W2085145661","https://openalex.org/W2091291136","https://openalex.org/W2091505154","https://openalex.org/W2103111465","https://openalex.org/W2130637303","https://openalex.org/W2183488495","https://openalex.org/W2989128237","https://openalex.org/W3142300713","https://openalex.org/W3194242537","https://openalex.org/W4212912562","https://openalex.org/W4212973943","https://openalex.org/W4231751431","https://openalex.org/W4243140258","https://openalex.org/W4247489173","https://openalex.org/W4285719527","https://openalex.org/W6635065579"],"related_works":["https://openalex.org/W3135285549","https://openalex.org/W2576451984","https://openalex.org/W3038055344","https://openalex.org/W1520600066","https://openalex.org/W1995723465","https://openalex.org/W3092127437","https://openalex.org/W2337407531","https://openalex.org/W2001264248","https://openalex.org/W2018228211","https://openalex.org/W1990787369"],"abstract_inverted_index":{"Random":[0],"perturbation":[1,20],"of":[2,21,61,68],"the":[3,22,40,66,69],"projected":[4,23],"variable":[5,24],"metric":[6,25],"method":[7,26],"for":[8,27,46],"nonsmooth":[9,31],"nonconvex":[10,34],"optimization":[11,35],"problems":[12],"with":[13],"linear":[14],"constraints":[15],"We":[16],"present":[17],"a":[18,43,47,58],"random":[19],"solving":[28],"linearly":[29],"constrained":[30],"(i.e.,":[32],"nondifferentiable)":[33],"problems,":[36],"and":[37],"we":[38],"establish":[39],"convergence":[41],"to":[42],"global":[44],"minimum":[45],"locally":[48],"Lipschitz":[49],"continuous":[50],"objective":[51],"function":[52],"which":[53],"may":[54],"be":[55],"nondifferentiable":[56],"on":[57],"countable":[59],"set":[60],"points.":[62],"Numerical":[63],"results":[64],"show":[65],"effectiveness":[67],"proposed":[70],"approach.":[71]},"counts_by_year":[{"year":2023,"cited_by_count":3},{"year":2019,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2013,"cited_by_count":1}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}