{"id":"https://openalex.org/W7123364426","doi":"https://doi.org/10.1109/cdc57313.2025.11312829","title":"Convergence rates of \u2113 <sub>q</sub> penalty methods for nonsmooth nonconvex optimization with nonlinear equality constraints","display_name":"Convergence rates of \u2113 <sub>q</sub> penalty methods for nonsmooth nonconvex optimization with nonlinear equality constraints","publication_year":2025,"publication_date":"2025-12-09","ids":{"openalex":"https://openalex.org/W7123364426","doi":"https://doi.org/10.1109/cdc57313.2025.11312829"},"language":null,"primary_location":{"id":"doi:10.1109/cdc57313.2025.11312829","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc57313.2025.11312829","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2025 IEEE 64th Conference on Decision and Control (CDC)","raw_type":"proceedings-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/A5061379779","display_name":"Lahcen El Bourkhissi","orcid":null},"institutions":[{"id":"https://openalex.org/I61641377","display_name":"Universitatea Na\u021bional\u0103 de \u0218tiin\u021b\u0103 \u0219i Tehnologie Politehnica Bucure\u0219ti","ror":"https://ror.org/0558j5q12","country_code":"RO","type":"education","lineage":["https://openalex.org/I61641377"]}],"countries":["RO"],"is_corresponding":true,"raw_author_name":"Lahcen El Bourkhissi","raw_affiliation_strings":["National University of Science and Technology Politehnica Bucharest,Department of Automatic Control and Systems Engineering,Bucharest,Romania,060042"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"National University of Science and Technology Politehnica Bucharest,Department of Automatic Control and Systems Engineering,Bucharest,Romania,060042","institution_ids":["https://openalex.org/I61641377"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5019114471","display_name":"Ion Necoara","orcid":"https://orcid.org/0000-0003-1102-2654"},"institutions":[{"id":"https://openalex.org/I61641377","display_name":"Universitatea Na\u021bional\u0103 de \u0218tiin\u021b\u0103 \u0219i Tehnologie Politehnica Bucure\u0219ti","ror":"https://ror.org/0558j5q12","country_code":"RO","type":"education","lineage":["https://openalex.org/I61641377"]}],"countries":["RO"],"is_corresponding":false,"raw_author_name":"Ion Necoara","raw_affiliation_strings":["National University of Science and Technology Politehnica Bucharest,Department of Automatic Control and Systems Engineering,Bucharest,Romania,060042"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"National University of Science and Technology Politehnica Bucharest,Department of Automatic Control and Systems Engineering,Bucharest,Romania,060042","institution_ids":["https://openalex.org/I61641377"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5061379779"],"corresponding_institution_ids":["https://openalex.org/I61641377"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.72944759,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"5348","last_page":"5353"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10545","display_name":"Optimization and Variational Analysis","score":0.2565999925136566,"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":0.2565999925136566,"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/T10791","display_name":"Advanced Control Systems Optimization","score":0.19089999794960022,"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":0.1808999925851822,"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/penalty-method","display_name":"Penalty method","score":0.8281000256538391},{"id":"https://openalex.org/keywords/differentiable-function","display_name":"Differentiable function","score":0.5439000129699707},{"id":"https://openalex.org/keywords/quadratic-equation","display_name":"Quadratic equation","score":0.5128999948501587},{"id":"https://openalex.org/keywords/optimal-control","display_name":"Optimal control","score":0.5037999749183655},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.49790000915527344},{"id":"https://openalex.org/keywords/iterated-function","display_name":"Iterated function","score":0.49630001187324524},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.49000000953674316},{"id":"https://openalex.org/keywords/augmented-lagrangian-method","display_name":"Augmented Lagrangian method","score":0.476500004529953},{"id":"https://openalex.org/keywords/norm","display_name":"Norm (philosophy)","score":0.45190000534057617},{"id":"https://openalex.org/keywords/constrained-optimization","display_name":"Constrained optimization","score":0.4489000141620636}],"concepts":[{"id":"https://openalex.org/C6180225","wikidata":"https://www.wikidata.org/wiki/Q3411771","display_name":"Penalty method","level":2,"score":0.8281000256538391},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6672999858856201},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.6225000023841858},{"id":"https://openalex.org/C202615002","wikidata":"https://www.wikidata.org/wiki/Q783507","display_name":"Differentiable function","level":2,"score":0.5439000129699707},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.5128999948501587},{"id":"https://openalex.org/C91575142","wikidata":"https://www.wikidata.org/wiki/Q1971426","display_name":"Optimal control","level":2,"score":0.5037999749183655},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.49790000915527344},{"id":"https://openalex.org/C140479938","wikidata":"https://www.wikidata.org/wiki/Q5254619","display_name":"Iterated function","level":2,"score":0.49630001187324524},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.49000000953674316},{"id":"https://openalex.org/C150452318","wikidata":"https://www.wikidata.org/wiki/Q4820432","display_name":"Augmented Lagrangian method","level":2,"score":0.476500004529953},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.45190000534057617},{"id":"https://openalex.org/C55660270","wikidata":"https://www.wikidata.org/wiki/Q5164377","display_name":"Constrained optimization","level":2,"score":0.4489000141620636},{"id":"https://openalex.org/C115527620","wikidata":"https://www.wikidata.org/wiki/Q769909","display_name":"Nonlinear programming","level":3,"score":0.44859999418258667},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.43389999866485596},{"id":"https://openalex.org/C2776135515","wikidata":"https://www.wikidata.org/wiki/Q17143721","display_name":"Regularization (linguistics)","level":2,"score":0.4246000051498413},{"id":"https://openalex.org/C189237950","wikidata":"https://www.wikidata.org/wiki/Q2500758","display_name":"Stationary point","level":2,"score":0.4007999897003174},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.38760000467300415},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.3874000012874603},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3675000071525574},{"id":"https://openalex.org/C2989514635","wikidata":"https://www.wikidata.org/wiki/Q5164377","display_name":"Constrained optimization problem","level":3,"score":0.3467999994754791},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.3398999869823456},{"id":"https://openalex.org/C2776330181","wikidata":"https://www.wikidata.org/wiki/Q18358244","display_name":"Maximization","level":2,"score":0.3260999917984009},{"id":"https://openalex.org/C147764199","wikidata":"https://www.wikidata.org/wiki/Q6865248","display_name":"Minification","level":2,"score":0.31380000710487366},{"id":"https://openalex.org/C63548660","wikidata":"https://www.wikidata.org/wiki/Q858223","display_name":"Limit point","level":2,"score":0.30970001220703125},{"id":"https://openalex.org/C198927703","wikidata":"https://www.wikidata.org/wiki/Q4373881","display_name":"Sequential quadratic programming","level":3,"score":0.30959999561309814},{"id":"https://openalex.org/C110639684","wikidata":"https://www.wikidata.org/wiki/Q20702","display_name":"Pendulum","level":2,"score":0.30730000138282776},{"id":"https://openalex.org/C2778646529","wikidata":"https://www.wikidata.org/wiki/Q16948724","display_name":"Nonlinear complementarity problem","level":4,"score":0.30720001459121704},{"id":"https://openalex.org/C192921069","wikidata":"https://www.wikidata.org/wiki/Q550134","display_name":"Inverted pendulum","level":3,"score":0.30219998955726624},{"id":"https://openalex.org/C177067428","wikidata":"https://www.wikidata.org/wiki/Q17013331","display_name":"Feasible region","level":2,"score":0.2919999957084656},{"id":"https://openalex.org/C81845259","wikidata":"https://www.wikidata.org/wiki/Q290117","display_name":"Quadratic programming","level":2,"score":0.2800000011920929},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.2743000090122223},{"id":"https://openalex.org/C2776036281","wikidata":"https://www.wikidata.org/wiki/Q48769818","display_name":"Constraint (computer-aided design)","level":2,"score":0.26969999074935913}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/cdc57313.2025.11312829","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc57313.2025.11312829","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2025 IEEE 64th Conference on Decision and Control (CDC)","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/16","score":0.7109872698783875,"display_name":"Peace, Justice and strong institutions"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"In":[0],"this":[1,22],"paper,":[2],"we":[3,24,91,116],"consider":[4],"nonsmooth":[5],"nonconvex":[6],"optimization":[7],"problems":[8],"with":[9],"nonlinear":[10],"equality":[11],"constraints":[12],"having":[13],"the":[14,39,42,46,49,56,60,71,79,88,94,124,127],"objective":[15],"function":[16,62],"in":[17,45,105],"composite":[18],"form.":[19],"To":[20],"solve":[21],"problem,":[23],"introduce":[25],"a":[26,65,74],"linearized":[27],"\u2113<inf":[28],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[29],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">q</inf>":[30],"penalty":[31,50,61],"method,":[32],"where":[33],"q":[34],"\u2208":[35],"(1,":[36],"2]":[37],"is":[38],"parameter":[40],"defining":[41],"norm":[43],"used":[44],"construction":[47],"of":[48,59,73,87,96,126],"function.":[51],"Our":[52],"method":[53,98],"involves":[54],"linearizing":[55],"differentiable":[57],"part":[58],"and":[63,122],"adding":[64],"quadratic":[66],"regularization.":[67],"This":[68],"approach":[69],"requires":[70],"computation":[72],"proximal":[75],"step,":[76],"which":[77],"becomes":[78],"next":[80],"iterate.":[81],"By":[82],"using":[83],"an":[84,101,135],"adaptive":[85],"choice":[86],"regularization":[89],"parameter,":[90],"establish":[92],"that":[93],"iterates":[95],"our":[97,118],"converge":[99],"to":[100],"\u03f5-first-order":[102],"stationary":[103],"point":[104],"$\\mathcal{O}\\left(":[106],"{1/{\\varepsilon":[107],"^{2(q":[108],"+":[109],"1)/q(q":[110],"-":[111],"1)}}}":[112],"\\right)$":[113],"iterations.":[114],"Finally,":[115],"put":[117],"theory":[119],"into":[120],"practice":[121],"evaluate":[123],"performance":[125],"proposed":[128],"algorithm":[129],"on":[130],"model":[131],"predictive":[132],"control":[133],"for":[134],"inverted":[136],"pendulum":[137],"system.":[138]},"counts_by_year":[],"updated_date":"2026-05-03T08:25:01.440150","created_date":"2026-01-14T00:00:00"}
