{"id":"https://openalex.org/W2290331402","doi":"https://doi.org/10.1109/cdc.2015.7402403","title":"On the behavior of first-order penalty methods for conic constrained convex programming when Lagrange multipliers do not exist","display_name":"On the behavior of first-order penalty methods for conic constrained convex programming when Lagrange multipliers do not exist","publication_year":2015,"publication_date":"2015-12-01","ids":{"openalex":"https://openalex.org/W2290331402","doi":"https://doi.org/10.1109/cdc.2015.7402403","mag":"2290331402"},"language":"en","primary_location":{"id":"doi:10.1109/cdc.2015.7402403","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc.2015.7402403","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2015 54th IEEE 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/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":true,"raw_author_name":"Ion Necoara","raw_affiliation_strings":["Automatic Control and Systems Engineering Department, University Politehnica Bucharest, Romania"],"affiliations":[{"raw_affiliation_string":"Automatic Control and Systems Engineering Department, University Politehnica Bucharest, Romania","institution_ids":["https://openalex.org/I61641377"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5049988389","display_name":"Andrei P\u0103tra\u015fcu","orcid":"https://orcid.org/0000-0002-9293-9386"},"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":"Andrei Patrascu","raw_affiliation_strings":["Automatic Control and Systems Engineering Department, University Politehnica Bucharest, Romania"],"affiliations":[{"raw_affiliation_string":"Automatic Control and Systems Engineering Department, University Politehnica Bucharest, Romania","institution_ids":["https://openalex.org/I61641377"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5019114471"],"corresponding_institution_ids":["https://openalex.org/I61641377"],"apc_list":null,"apc_paid":null,"fwci":0.3236,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.63247511,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":null,"issue":null,"first_page":"1378","last_page":"1383"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9991999864578247,"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"}},"topics":[{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9991999864578247,"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"}},{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9991999864578247,"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/T11612","display_name":"Stochastic Gradient Optimization Techniques","score":0.9991000294685364,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/penalty-method","display_name":"Penalty method","score":0.8312826156616211},{"id":"https://openalex.org/keywords/lagrange-multiplier","display_name":"Lagrange multiplier","score":0.7312250137329102},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.7032526135444641},{"id":"https://openalex.org/keywords/augmented-lagrangian-method","display_name":"Augmented Lagrangian method","score":0.6666224598884583},{"id":"https://openalex.org/keywords/conic-section","display_name":"Conic section","score":0.6195006966590881},{"id":"https://openalex.org/keywords/conic-optimization","display_name":"Conic optimization","score":0.5769906044006348},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5756031274795532},{"id":"https://openalex.org/keywords/quadratic-equation","display_name":"Quadratic equation","score":0.5579795837402344},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.4846942722797394},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.47047215700149536},{"id":"https://openalex.org/keywords/quadratic-programming","display_name":"Quadratic programming","score":0.4615263044834137},{"id":"https://openalex.org/keywords/convex-function","display_name":"Convex function","score":0.45875951647758484},{"id":"https://openalex.org/keywords/rate-of-convergence","display_name":"Rate of convergence","score":0.44530290365219116},{"id":"https://openalex.org/keywords/constraint","display_name":"Constraint (computer-aided design)","score":0.4422367811203003},{"id":"https://openalex.org/keywords/convex-optimization","display_name":"Convex optimization","score":0.4351472854614258},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.4291476011276245},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.39824989438056946},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3198547959327698},{"id":"https://openalex.org/keywords/convex-combination","display_name":"Convex combination","score":0.20282673835754395},{"id":"https://openalex.org/keywords/key","display_name":"Key (lock)","score":0.11737969517707825}],"concepts":[{"id":"https://openalex.org/C6180225","wikidata":"https://www.wikidata.org/wiki/Q3411771","display_name":"Penalty method","level":2,"score":0.8312826156616211},{"id":"https://openalex.org/C73684929","wikidata":"https://www.wikidata.org/wiki/Q598870","display_name":"Lagrange multiplier","level":2,"score":0.7312250137329102},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.7032526135444641},{"id":"https://openalex.org/C150452318","wikidata":"https://www.wikidata.org/wiki/Q4820432","display_name":"Augmented Lagrangian method","level":2,"score":0.6666224598884583},{"id":"https://openalex.org/C108598597","wikidata":"https://www.wikidata.org/wiki/Q124255","display_name":"Conic section","level":2,"score":0.6195006966590881},{"id":"https://openalex.org/C79187972","wikidata":"https://www.wikidata.org/wiki/Q2654791","display_name":"Conic optimization","level":5,"score":0.5769906044006348},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5756031274795532},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.5579795837402344},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.4846942722797394},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.47047215700149536},{"id":"https://openalex.org/C81845259","wikidata":"https://www.wikidata.org/wiki/Q290117","display_name":"Quadratic programming","level":2,"score":0.4615263044834137},{"id":"https://openalex.org/C145446738","wikidata":"https://www.wikidata.org/wiki/Q319913","display_name":"Convex function","level":3,"score":0.45875951647758484},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.44530290365219116},{"id":"https://openalex.org/C2776036281","wikidata":"https://www.wikidata.org/wiki/Q48769818","display_name":"Constraint (computer-aided design)","level":2,"score":0.4422367811203003},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.4351472854614258},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.4291476011276245},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.39824989438056946},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3198547959327698},{"id":"https://openalex.org/C111110010","wikidata":"https://www.wikidata.org/wiki/Q2627315","display_name":"Convex combination","level":4,"score":0.20282673835754395},{"id":"https://openalex.org/C26517878","wikidata":"https://www.wikidata.org/wiki/Q228039","display_name":"Key (lock)","level":2,"score":0.11737969517707825},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0},{"id":"https://openalex.org/C38652104","wikidata":"https://www.wikidata.org/wiki/Q3510521","display_name":"Computer security","level":1,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","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/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/cdc.2015.7402403","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc.2015.7402403","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2015 54th IEEE Conference on Decision and Control (CDC)","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Peace, Justice and strong institutions","score":0.7799999713897705,"id":"https://metadata.un.org/sdg/16"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":16,"referenced_works":["https://openalex.org/W1963529497","https://openalex.org/W1980145158","https://openalex.org/W1981832695","https://openalex.org/W1993569878","https://openalex.org/W2030121914","https://openalex.org/W2030161963","https://openalex.org/W2033121805","https://openalex.org/W2042860556","https://openalex.org/W2060649248","https://openalex.org/W2092937927","https://openalex.org/W2094336028","https://openalex.org/W2129470876","https://openalex.org/W2144603975","https://openalex.org/W2167732364","https://openalex.org/W2963183767","https://openalex.org/W4244633107"],"related_works":["https://openalex.org/W2015060724","https://openalex.org/W3199026565","https://openalex.org/W2058578573","https://openalex.org/W2012871340","https://openalex.org/W3046535663","https://openalex.org/W4323321439","https://openalex.org/W4313189992","https://openalex.org/W3105202832","https://openalex.org/W2030716009","https://openalex.org/W2017965889"],"abstract_inverted_index":{"In":[0],"this":[1,35],"paper":[2],"we":[3,37,108],"analyze":[4],"the":[5,26,29,41,51,55,61,67,96,103],"numerical":[6],"behavior":[7],"of":[8,28,43,54,66,80,85,95],"first-order":[9],"quadratic":[10,57],"penalty":[11,32,58,63,97],"methods":[12],"for":[13,90],"solving":[14],"large-scale":[15],"conic":[16],"constrained":[17],"convex":[18],"problems":[19],"with":[20],"composite":[21,104],"objective":[22,105],"function.":[23,106],"Contrary":[24],"to":[25],"most":[27],"results":[30,82],"on":[31,102,110],"methods,":[33],"in":[34,83],"work":[36],"do":[38],"not":[39],"assume":[40],"existence":[42],"a":[44,111],"finite":[45],"optimal":[46],"Lagrange":[47],"multiplier.":[48],"We":[49,77],"derive":[50],"iteration":[52],"complexity":[53,116],"classical":[56],"method,":[59],"where":[60],"corresponding":[62],"regularized":[64],"formulation":[65],"original":[68],"problem":[69],"is":[70],"solved":[71],"using":[72],"Nesterov's":[73],"fast":[74],"gradient":[75],"algorithm.":[76],"provide":[78],"rate":[79],"convergence":[81],"terms":[84],"feasibility":[86],"violation":[87],"and":[88,92],"suboptimality":[89],"adaptive":[91],"non-adaptive":[93],"variants":[94],"scheme,":[98],"under":[99],"various":[100],"assumptions":[101],"Finally,":[107],"show":[109],"simple":[112],"example":[113],"that":[114],"our":[115],"estimates":[117],"are":[118],"tight.":[119]},"counts_by_year":[{"year":2017,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
