{"id":"https://openalex.org/W4411565492","doi":"https://doi.org/10.3390/axioms14070488","title":"A Penalty Approach for Solving Generalized Absolute Value Equations","display_name":"A Penalty Approach for Solving Generalized Absolute Value Equations","publication_year":2025,"publication_date":"2025-06-22","ids":{"openalex":"https://openalex.org/W4411565492","doi":"https://doi.org/10.3390/axioms14070488"},"language":"en","primary_location":{"id":"doi:10.3390/axioms14070488","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms14070488","pdf_url":null,"source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Axioms","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://doi.org/10.3390/axioms14070488","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5068077891","display_name":"Zahira Kebaili","orcid":null},"institutions":[{"id":"https://openalex.org/I40193446","display_name":"University Ferhat Abbas of Setif","ror":"https://ror.org/02rzqza52","country_code":"DZ","type":"education","lineage":["https://openalex.org/I40193446"]}],"countries":["DZ"],"is_corresponding":true,"raw_author_name":"Zahira Kebaili","raw_affiliation_strings":["Fundamental and Numerical Laboratory (MFNL), Department of Mathematics, Faculty of Sciences, Ferhat Abbas Setif-1 University, Algeria Setif 19000, Algeria"],"affiliations":[{"raw_affiliation_string":"Fundamental and Numerical Laboratory (MFNL), Department of Mathematics, Faculty of Sciences, Ferhat Abbas Setif-1 University, Algeria Setif 19000, Algeria","institution_ids":["https://openalex.org/I40193446"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5071200493","display_name":"Hassina Grar","orcid":null},"institutions":[{"id":"https://openalex.org/I40193446","display_name":"University Ferhat Abbas of Setif","ror":"https://ror.org/02rzqza52","country_code":"DZ","type":"education","lineage":["https://openalex.org/I40193446"]}],"countries":["DZ"],"is_corresponding":false,"raw_author_name":"Hassina Grar","raw_affiliation_strings":["Fundamental and Numerical Laboratory (MFNL), Department of Mathematics, Faculty of Sciences, Ferhat Abbas Setif-1 University, Algeria Setif 19000, Algeria"],"affiliations":[{"raw_affiliation_string":"Fundamental and Numerical Laboratory (MFNL), Department of Mathematics, Faculty of Sciences, Ferhat Abbas Setif-1 University, Algeria Setif 19000, Algeria","institution_ids":["https://openalex.org/I40193446"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100338763","display_name":"Mohamed Achache","orcid":"https://orcid.org/0009-0007-4153-3371"},"institutions":[{"id":"https://openalex.org/I40193446","display_name":"University Ferhat Abbas of Setif","ror":"https://ror.org/02rzqza52","country_code":"DZ","type":"education","lineage":["https://openalex.org/I40193446"]}],"countries":["DZ"],"is_corresponding":false,"raw_author_name":"Mohamed Achache","raw_affiliation_strings":["Fundamental and Numerical Laboratory (MFNL), Department of Mathematics, Faculty of Sciences, Ferhat Abbas Setif-1 University, Algeria Setif 19000, Algeria"],"affiliations":[{"raw_affiliation_string":"Fundamental and Numerical Laboratory (MFNL), Department of Mathematics, Faculty of Sciences, Ferhat Abbas Setif-1 University, Algeria Setif 19000, Algeria","institution_ids":["https://openalex.org/I40193446"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5068077891"],"corresponding_institution_ids":["https://openalex.org/I40193446"],"apc_list":{"value":1400,"currency":"CHF","value_usd":1515},"apc_paid":{"value":1400,"currency":"CHF","value_usd":1515},"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.2577701,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"14","issue":"7","first_page":"488","last_page":"488"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9983999729156494,"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":0.9983999729156494,"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/T10792","display_name":"Matrix Theory and Algorithms","score":0.9976000189781189,"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/T13487","display_name":"Statistical and numerical algorithms","score":0.9853000044822693,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/absolute","display_name":"Absolute (philosophy)","score":0.6444178223609924},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6154239773750305},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5142301917076111},{"id":"https://openalex.org/keywords/value","display_name":"Value (mathematics)","score":0.5138578414916992},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.34935885667800903},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.1789766550064087},{"id":"https://openalex.org/keywords/philosophy","display_name":"Philosophy","score":0.0482652485370636}],"concepts":[{"id":"https://openalex.org/C2777487392","wikidata":"https://www.wikidata.org/wiki/Q481201","display_name":"Absolute (philosophy)","level":2,"score":0.6444178223609924},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6154239773750305},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5142301917076111},{"id":"https://openalex.org/C2776291640","wikidata":"https://www.wikidata.org/wiki/Q2912517","display_name":"Value (mathematics)","level":2,"score":0.5138578414916992},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.34935885667800903},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.1789766550064087},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0482652485370636},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.3390/axioms14070488","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms14070488","pdf_url":null,"source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Axioms","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:339f79c88f2148c589c2792996b81861","is_oa":true,"landing_page_url":"https://doaj.org/article/339f79c88f2148c589c2792996b81861","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Axioms, Vol 14, Iss 7, p 488 (2025)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3390/axioms14070488","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms14070488","pdf_url":null,"source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Axioms","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":20,"referenced_works":["https://openalex.org/W1950693819","https://openalex.org/W1968411180","https://openalex.org/W1985813549","https://openalex.org/W2009758399","https://openalex.org/W2013760236","https://openalex.org/W2023548950","https://openalex.org/W2031293992","https://openalex.org/W2053227127","https://openalex.org/W2071515819","https://openalex.org/W2100762546","https://openalex.org/W2134508021","https://openalex.org/W2135600319","https://openalex.org/W2225225175","https://openalex.org/W2783469840","https://openalex.org/W2803268134","https://openalex.org/W2926190368","https://openalex.org/W4285653872","https://openalex.org/W4285765289","https://openalex.org/W4313531411","https://openalex.org/W4322501137"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W2498348907","https://openalex.org/W1979597421","https://openalex.org/W2985905814","https://openalex.org/W2007980826","https://openalex.org/W2262959435","https://openalex.org/W4229515626","https://openalex.org/W3202488475","https://openalex.org/W4246922841","https://openalex.org/W2728714032"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"we":[3,21,59],"propose":[4],"a":[5,43,49,56],"penalty":[6,50,75],"approach":[7,102],"for":[8],"solving":[9],"generalized":[10],"absolute":[11],"value":[12],"equations":[13,47],"(GAVEs)":[14],"of":[15,45,64,71],"the":[16,23,39,62,65,74],"type":[17],"Ax\u2212B|x|=b,":[18],"(A,B\u2208Rn\u00d7n,b\u2208Rn).":[19],"Firstly,":[20],"reformulate":[22],"GAVEs":[24],"as":[25],"variational":[26,41],"inequality":[27],"problems":[28],"passing":[29],"through":[30],"an":[31],"equivalent":[32],"horizontal":[33],"linear":[34],"complementarity":[35],"problem.":[36],"To":[37],"approximate":[38],"resulting":[40],"inequality,":[42],"sequence":[44,67],"nonlinear":[46],"containing":[48],"term":[51],"is":[52,82,103],"then":[53],"defined.":[54],"Under":[55],"mild":[57],"assumption,":[58],"show":[60,99],"that":[61,70,100],"solution":[63],"considered":[66],"converges":[68],"to":[69,78,98],"GAVE":[72],"if":[73],"parameter":[76],"tends":[77],"infinity.":[79],"An":[80],"algorithm":[81],"developed":[83],"where":[84],"its":[85],"corresponding":[86],"theoretical":[87],"arguments":[88],"are":[89,96],"well":[90],"established.":[91],"Finally,":[92],"some":[93],"numerical":[94],"experiments":[95],"presented":[97],"our":[101],"quite":[104],"appreciable.":[105]},"counts_by_year":[],"updated_date":"2026-02-27T16:54:17.756197","created_date":"2025-10-10T00:00:00"}
