{"id":"https://openalex.org/W3037503223","doi":"https://doi.org/10.1109/dessert50317.2020.9125035","title":"Regularization Method for the Clarke\u2019s Generalized Jacobian to Ensure the Formation of Nonsingular Systems for Inexact Newton Methods","display_name":"Regularization Method for the Clarke\u2019s Generalized Jacobian to Ensure the Formation of Nonsingular Systems for Inexact Newton Methods","publication_year":2020,"publication_date":"2020-05-01","ids":{"openalex":"https://openalex.org/W3037503223","doi":"https://doi.org/10.1109/dessert50317.2020.9125035","mag":"3037503223"},"language":"en","primary_location":{"id":"doi:10.1109/dessert50317.2020.9125035","is_oa":false,"landing_page_url":"https://doi.org/10.1109/dessert50317.2020.9125035","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2020 IEEE 11th International Conference on Dependable Systems, Services and Technologies (DESSERT)","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/A5069144524","display_name":"Sergii Saukh","orcid":"https://orcid.org/0000-0001-7658-0839"},"institutions":[{"id":"https://openalex.org/I4210090521","display_name":"Pukhov Institute for Modelling in Energy Engineering","ror":"https://ror.org/00fhten74","country_code":"UA","type":"facility","lineage":["https://openalex.org/I149851306","https://openalex.org/I4210090521"]}],"countries":["UA"],"is_corresponding":true,"raw_author_name":"Sergii Saukh","raw_affiliation_strings":["Department of Mathematical and Econometric Modelling, Pukhov Institute for Modelling in Energy Engineering, Kyiv, Ukraine"],"affiliations":[{"raw_affiliation_string":"Department of Mathematical and Econometric Modelling, Pukhov Institute for Modelling in Energy Engineering, Kyiv, Ukraine","institution_ids":["https://openalex.org/I4210090521"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5069144524"],"corresponding_institution_ids":["https://openalex.org/I4210090521"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.06634402,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"103","issue":null,"first_page":"363","last_page":"370"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T14083","display_name":"Extremum Seeking Control Systems","score":0.9994999766349792,"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"}},"topics":[{"id":"https://openalex.org/T14083","display_name":"Extremum Seeking Control Systems","score":0.9994999766349792,"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/T10791","display_name":"Advanced Control Systems Optimization","score":0.9991999864578247,"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":0.9959999918937683,"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/jacobian-matrix-and-determinant","display_name":"Jacobian matrix and determinant","score":0.9065603017807007},{"id":"https://openalex.org/keywords/invertible-matrix","display_name":"Invertible matrix","score":0.8554426431655884},{"id":"https://openalex.org/keywords/regularization","display_name":"Regularization (linguistics)","score":0.621043860912323},{"id":"https://openalex.org/keywords/newtons-method","display_name":"Newton's method","score":0.6207789778709412},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5158045291900635},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4964054226875305},{"id":"https://openalex.org/keywords/quasi-newton-method","display_name":"Quasi-Newton method","score":0.4370811879634857},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.4223890006542206},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.41165655851364136},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3648703694343567},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.18203997611999512},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.09500536322593689},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.06423163414001465},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.058287978172302246}],"concepts":[{"id":"https://openalex.org/C200331156","wikidata":"https://www.wikidata.org/wiki/Q506041","display_name":"Jacobian matrix and determinant","level":2,"score":0.9065603017807007},{"id":"https://openalex.org/C96442724","wikidata":"https://www.wikidata.org/wiki/Q242188","display_name":"Invertible matrix","level":2,"score":0.8554426431655884},{"id":"https://openalex.org/C2776135515","wikidata":"https://www.wikidata.org/wiki/Q17143721","display_name":"Regularization (linguistics)","level":2,"score":0.621043860912323},{"id":"https://openalex.org/C85189116","wikidata":"https://www.wikidata.org/wiki/Q374195","display_name":"Newton's method","level":3,"score":0.6207789778709412},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5158045291900635},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4964054226875305},{"id":"https://openalex.org/C114954040","wikidata":"https://www.wikidata.org/wiki/Q1476018","display_name":"Quasi-Newton method","level":4,"score":0.4370811879634857},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4223890006542206},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.41165655851364136},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3648703694343567},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.18203997611999512},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.09500536322593689},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.06423163414001465},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.058287978172302246},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/dessert50317.2020.9125035","is_oa":false,"landing_page_url":"https://doi.org/10.1109/dessert50317.2020.9125035","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2020 IEEE 11th International Conference on Dependable Systems, Services and Technologies (DESSERT)","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":25,"referenced_works":["https://openalex.org/W42857015","https://openalex.org/W84287112","https://openalex.org/W1510093334","https://openalex.org/W1543439990","https://openalex.org/W1972028349","https://openalex.org/W2001024683","https://openalex.org/W2008668719","https://openalex.org/W2047905441","https://openalex.org/W2047959957","https://openalex.org/W2068060907","https://openalex.org/W2088055586","https://openalex.org/W2090689930","https://openalex.org/W2119279696","https://openalex.org/W2151902790","https://openalex.org/W2185325708","https://openalex.org/W2596636257","https://openalex.org/W2790400697","https://openalex.org/W2922112709","https://openalex.org/W2971158479","https://openalex.org/W2999912265","https://openalex.org/W4253572364","https://openalex.org/W4301791716","https://openalex.org/W6630536125","https://openalex.org/W6672749837","https://openalex.org/W6686741959"],"related_works":["https://openalex.org/W1896162644","https://openalex.org/W3040723915","https://openalex.org/W1901133132","https://openalex.org/W2068966571","https://openalex.org/W2127159799","https://openalex.org/W2144504157","https://openalex.org/W2385824356","https://openalex.org/W2741623878","https://openalex.org/W2083618095","https://openalex.org/W2016630321"],"abstract_inverted_index":{"Finding":[0],"solutions":[1],"to":[2,16,118,133,188,202],"big":[3,155],"data":[4,156],"optimization":[5,157],"problems":[6,158,185,199],"requires":[7],"the":[8,21,24,29,32,36,43,47,50,54,65,77,80,84,89,92,95,104,109,129,135,170,177],"using":[9],"of":[10,23,31,49,64,79,83,94,103,108,137,176,200],"numerical":[11],"methods":[12],"that":[13,42,116,159],"are":[14,53],"resistant":[15],"calculation":[17],"errors.":[18],"We":[19,39,113,144],"analyze":[20],"impact":[22],"computation":[25],"errors":[26,44,90],"caused":[27],"by":[28],"use":[30],"Fischer-Burmeister":[33,110],"function":[34,52,97],"on":[35,169],"PATH":[37,85,194],"algorithm.":[38,86],"found":[40],"out":[41],"in":[45,91,120],"calculating":[46],"gradient":[48,81],"merit":[51,96,111],"main":[55],"cause":[56],"for":[57,71,128,140,165],"slowing":[58],"down":[59],"and":[60,123],"even":[61],"loosing":[62],"convergence":[63],"minor":[66],"iterative":[67],"cycle":[68],"when":[69],"searching":[70],"a":[72,101,125],"new":[73],"decision":[74],"point":[75],"along":[76],"direction":[78],"descent":[82],"To":[87],"counteract":[88],"evaluation":[93],"gradient,":[98],"we":[99,153],"propose":[100,124],"regularization":[102,126,147,175],"Clarke\u2019s":[105,130,178],"generalized":[106,131,179],"Jacobian":[107,132,180],"function.":[112],"establish":[114],"conditions":[115],"lead":[117],"singularity":[119],"Newton\u2019s":[121],"systems":[122,139],"method":[127,148,173],"ensure":[134],"formation":[136],"nonsingular":[138],"inexact":[141],"Newton":[142],"methods.":[143],"compare":[145],"our":[146,181],"against":[149],"state-of-the-art":[150],"benchmarks.":[151],"Specifically,":[152],"solve":[154],"originate":[160],"from":[161],"electricity":[162],"market":[163],"models":[164],"different":[166],"countries.":[167],"Based":[168],"preconditioned":[171],"quasi-Newton":[172],"with":[174,186],"implementation":[182],"successfully":[183],"solves":[184],"up":[187,201],"ten":[189,203],"million":[190],"dimensions.":[191],"By":[192],"contrast,":[193],"solver":[195],"allows":[196],"solving":[197],"similar":[198],"thousands":[204],"dimensions":[205],"only.":[206]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}