{"id":"https://openalex.org/W3109408437","doi":"https://doi.org/10.1109/icca51439.2020.9264376","title":"Log-sum-exp Optimization based on Continuous Piecewise Linearization Techniques","display_name":"Log-sum-exp Optimization based on Continuous Piecewise Linearization Techniques","publication_year":2020,"publication_date":"2020-10-09","ids":{"openalex":"https://openalex.org/W3109408437","doi":"https://doi.org/10.1109/icca51439.2020.9264376","mag":"3109408437"},"language":"en","primary_location":{"id":"doi:10.1109/icca51439.2020.9264376","is_oa":false,"landing_page_url":"https://doi.org/10.1109/icca51439.2020.9264376","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2020 IEEE 16th International Conference on Control & Automation (ICCA)","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/A5026806744","display_name":"Xiangming Xi","orcid":null},"institutions":[{"id":"https://openalex.org/I204983213","display_name":"Harbin Institute of Technology","ror":"https://ror.org/01yqg2h08","country_code":"CN","type":"education","lineage":["https://openalex.org/I204983213"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Xiangming Xi","raw_affiliation_strings":["School of Mechanical Engineering and Automation, Harbin Institute of Technology (Shenzhen), Shenzhen, China"],"affiliations":[{"raw_affiliation_string":"School of Mechanical Engineering and Automation, Harbin Institute of Technology (Shenzhen), Shenzhen, China","institution_ids":["https://openalex.org/I204983213"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5040253195","display_name":"Jun Xu","orcid":"https://orcid.org/0000-0002-2934-4814"},"institutions":[{"id":"https://openalex.org/I204983213","display_name":"Harbin Institute of Technology","ror":"https://ror.org/01yqg2h08","country_code":"CN","type":"education","lineage":["https://openalex.org/I204983213"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jun Xu","raw_affiliation_strings":["School of Mechanical Engineering and Automation, Harbin Institute of Technology (Shenzhen), Shenzhen, China"],"affiliations":[{"raw_affiliation_string":"School of Mechanical Engineering and Automation, Harbin Institute of Technology (Shenzhen), Shenzhen, China","institution_ids":["https://openalex.org/I204983213"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5087749601","display_name":"Yunjiang Lou","orcid":"https://orcid.org/0000-0001-8203-7795"},"institutions":[{"id":"https://openalex.org/I204983213","display_name":"Harbin Institute of Technology","ror":"https://ror.org/01yqg2h08","country_code":"CN","type":"education","lineage":["https://openalex.org/I204983213"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yunjiang Lou","raw_affiliation_strings":["School of Mechanical Engineering and Automation, Harbin Institute of Technology (Shenzhen), Shenzhen, China"],"affiliations":[{"raw_affiliation_string":"School of Mechanical Engineering and Automation, Harbin Institute of Technology (Shenzhen), Shenzhen, China","institution_ids":["https://openalex.org/I204983213"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5026806744"],"corresponding_institution_ids":["https://openalex.org/I204983213"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.1604357,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":95},"biblio":{"volume":null,"issue":null,"first_page":"600","last_page":"605"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10320","display_name":"Neural Networks and Applications","score":0.9990000128746033,"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"}},"topics":[{"id":"https://openalex.org/T10320","display_name":"Neural Networks and Applications","score":0.9990000128746033,"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"}},{"id":"https://openalex.org/T12111","display_name":"Industrial Vision Systems and Defect Detection","score":0.9983000159263611,"subfield":{"id":"https://openalex.org/subfields/2209","display_name":"Industrial and Manufacturing 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/T10057","display_name":"Face and Expression Recognition","score":0.995199978351593,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"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/softmax-function","display_name":"Softmax function","score":0.7097000479698181},{"id":"https://openalex.org/keywords/piecewise-linear-function","display_name":"Piecewise linear function","score":0.5896104574203491},{"id":"https://openalex.org/keywords/linearization","display_name":"Linearization","score":0.564993143081665},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5522980093955994},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5228529572486877},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.5092471837997437},{"id":"https://openalex.org/keywords/linear-programming","display_name":"Linear programming","score":0.49325698614120483},{"id":"https://openalex.org/keywords/convexity","display_name":"Convexity","score":0.4677828550338745},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4564090669155121},{"id":"https://openalex.org/keywords/piecewise","display_name":"Piecewise","score":0.44924160838127136},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.34768009185791016},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.34762513637542725},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.2858414947986603},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.14974981546401978}],"concepts":[{"id":"https://openalex.org/C188441871","wikidata":"https://www.wikidata.org/wiki/Q7554146","display_name":"Softmax function","level":3,"score":0.7097000479698181},{"id":"https://openalex.org/C17095337","wikidata":"https://www.wikidata.org/wiki/Q2375229","display_name":"Piecewise linear function","level":2,"score":0.5896104574203491},{"id":"https://openalex.org/C11210021","wikidata":"https://www.wikidata.org/wiki/Q1520713","display_name":"Linearization","level":3,"score":0.564993143081665},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5522980093955994},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5228529572486877},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.5092471837997437},{"id":"https://openalex.org/C41045048","wikidata":"https://www.wikidata.org/wiki/Q202843","display_name":"Linear programming","level":2,"score":0.49325698614120483},{"id":"https://openalex.org/C72134830","wikidata":"https://www.wikidata.org/wiki/Q5166524","display_name":"Convexity","level":2,"score":0.4677828550338745},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4564090669155121},{"id":"https://openalex.org/C164660894","wikidata":"https://www.wikidata.org/wiki/Q2037833","display_name":"Piecewise","level":2,"score":0.44924160838127136},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.34768009185791016},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.34762513637542725},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.2858414947986603},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.14974981546401978},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C106159729","wikidata":"https://www.wikidata.org/wiki/Q2294553","display_name":"Financial economics","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/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","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/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/icca51439.2020.9264376","is_oa":false,"landing_page_url":"https://doi.org/10.1109/icca51439.2020.9264376","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2020 IEEE 16th International Conference on Control & Automation (ICCA)","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":18,"referenced_works":["https://openalex.org/W1964191893","https://openalex.org/W1973161156","https://openalex.org/W1987793616","https://openalex.org/W2070938475","https://openalex.org/W2074551798","https://openalex.org/W2133161531","https://openalex.org/W2472357683","https://openalex.org/W2474772569","https://openalex.org/W2526006527","https://openalex.org/W2567105891","https://openalex.org/W2755028754","https://openalex.org/W2799332695","https://openalex.org/W2913125146","https://openalex.org/W2963941964","https://openalex.org/W2979612741","https://openalex.org/W3120740533","https://openalex.org/W3125330224","https://openalex.org/W6768615038"],"related_works":["https://openalex.org/W3107204728","https://openalex.org/W2133947431","https://openalex.org/W2490196280","https://openalex.org/W3182827720","https://openalex.org/W1596838019","https://openalex.org/W3208509670","https://openalex.org/W2109304297","https://openalex.org/W2100864966","https://openalex.org/W2083709218","https://openalex.org/W4323366562"],"abstract_inverted_index":{"The":[0],"log-sum-exp":[1,36],"(LSE)":[2],"function":[3],"is":[4],"a":[5,58,93,125],"class":[6],"of":[7,48,60,95,103],"important":[8],"non-linear":[9],"functions":[10,68],"that":[11],"has":[12],"been":[13],"widely":[14],"applied":[15],"in":[16],"many":[17],"fields,":[18],"such":[19],"as":[20,113,115],"the":[21,35,44,72,101,104,116,130],"signomial":[22],"geometric":[23],"optimization,":[24],"deep":[25],"neural":[26,122],"networks,":[27],"etc.":[28],"In":[29,40],"this":[30],"paper,":[31],"we":[32,51,86,107],"systematically":[33],"investigate":[34],"optimization":[37],"(LSEO)":[38],"methods.":[39],"order":[41],"to":[42],"handle":[43],"non-linearity":[45],"and":[46,129],"non-convexity":[47],"LSEO":[49],"problems,":[50],"propose":[52,87],"an":[53,88],"iterative":[54],"algorithm":[55,90],"by":[56],"optimizing":[57],"series":[59,94],"continuous":[61,73],"piecewise":[62,74],"linear":[63,75,96],"(CPWL)":[64],"problems":[65,80],"where":[66],"LSE":[67],"are":[69],"approximated":[70],"using":[71],"technique.":[76],"Since":[77],"CPWL":[78],"concave":[79],"have":[81],"some":[82,110],"useful":[83],"structural":[84],"properties,":[85],"efficient":[89],"which":[91],"solves":[92],"programming":[97],"problems.":[98],"To":[99],"confirm":[100],"validity":[102],"proposed":[105],"method,":[106],"test":[108],"on":[109,120],"toy":[111],"examples,":[112],"well":[114],"multi-class":[117],"classification":[118],"based":[119],"artificial":[121],"networks":[123],"with":[124],"softmax":[126],"output":[127],"layer":[128],"cross-entropy":[131],"loss":[132],"function.":[133]},"counts_by_year":[{"year":2025,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}