{"id":"https://openalex.org/W3177118562","doi":"https://doi.org/10.1145/3449639.3459289","title":"Convergence rate of the (1+1)-evolution strategy with success-based step-size adaptation on convex quadratic functions","display_name":"Convergence rate of the (1+1)-evolution strategy with success-based step-size adaptation on convex quadratic functions","publication_year":2021,"publication_date":"2021-06-21","ids":{"openalex":"https://openalex.org/W3177118562","doi":"https://doi.org/10.1145/3449639.3459289","mag":"3177118562"},"language":"en","primary_location":{"id":"doi:10.1145/3449639.3459289","is_oa":true,"landing_page_url":"https://doi.org/10.1145/3449639.3459289","pdf_url":"https://dl.acm.org/action/downloadSupplement?doi=10.1145%2F3449639.3459289&file=p1169-morinaga.pdf","source":{"id":"https://openalex.org/S4363608932","display_name":"Proceedings of the Genetic and Evolutionary Computation Conference","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"conference"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the Genetic and Evolutionary Computation Conference","raw_type":"proceedings-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://dl.acm.org/action/downloadSupplement?doi=10.1145%2F3449639.3459289&file=p1169-morinaga.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5065265296","display_name":"Daiki Morinaga","orcid":"https://orcid.org/0009-0009-7937-7567"},"institutions":[{"id":"https://openalex.org/I146399215","display_name":"University of Tsukuba","ror":"https://ror.org/02956yf07","country_code":"JP","type":"education","lineage":["https://openalex.org/I146399215"]}],"countries":["JP"],"is_corresponding":true,"raw_author_name":"Daiki Morinaga","raw_affiliation_strings":["University of Tsukuba, Tsukuba, Ibaraki, Japan"],"affiliations":[{"raw_affiliation_string":"University of Tsukuba, Tsukuba, Ibaraki, Japan","institution_ids":["https://openalex.org/I146399215"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5008914720","display_name":"Kazuto Fukuchi","orcid":"https://orcid.org/0000-0003-3895-219X"},"institutions":[{"id":"https://openalex.org/I146399215","display_name":"University of Tsukuba","ror":"https://ror.org/02956yf07","country_code":"JP","type":"education","lineage":["https://openalex.org/I146399215"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Kazuto Fukuchi","raw_affiliation_strings":["University of Tsukuba, Tsukuba, Ibaraki, Japan"],"affiliations":[{"raw_affiliation_string":"University of Tsukuba, Tsukuba, Ibaraki, Japan","institution_ids":["https://openalex.org/I146399215"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5022139141","display_name":"Jun Sakuma","orcid":"https://orcid.org/0000-0001-5015-3812"},"institutions":[{"id":"https://openalex.org/I146399215","display_name":"University of Tsukuba","ror":"https://ror.org/02956yf07","country_code":"JP","type":"education","lineage":["https://openalex.org/I146399215"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Jun Sakuma","raw_affiliation_strings":["University of Tsukuba, Tsukuba, Ibaraki, Japan"],"affiliations":[{"raw_affiliation_string":"University of Tsukuba, Tsukuba, Ibaraki, Japan","institution_ids":["https://openalex.org/I146399215"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5038757231","display_name":"Youhei Akimoto","orcid":"https://orcid.org/0000-0003-2760-8123"},"institutions":[{"id":"https://openalex.org/I146399215","display_name":"University of Tsukuba","ror":"https://ror.org/02956yf07","country_code":"JP","type":"education","lineage":["https://openalex.org/I146399215"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Youhei Akimoto","raw_affiliation_strings":["University of Tsukuba, Tsukuba, Ibaraki, Japan"],"affiliations":[{"raw_affiliation_string":"University of Tsukuba, Tsukuba, Ibaraki, Japan","institution_ids":["https://openalex.org/I146399215"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5065265296"],"corresponding_institution_ids":["https://openalex.org/I146399215"],"apc_list":null,"apc_paid":null,"fwci":1.0159,"has_fulltext":true,"cited_by_count":8,"citation_normalized_percentile":{"value":0.79667436,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11612","display_name":"Stochastic Gradient Optimization Techniques","score":0.996399998664856,"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/T11612","display_name":"Stochastic Gradient Optimization Techniques","score":0.996399998664856,"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/T10100","display_name":"Metaheuristic Optimization Algorithms Research","score":0.9926000237464905,"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/T10249","display_name":"Distributed Control Multi-Agent Systems","score":0.9921000003814697,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"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/hessian-matrix","display_name":"Hessian matrix","score":0.735491931438446},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6935430765151978},{"id":"https://openalex.org/keywords/rate-of-convergence","display_name":"Rate of convergence","score":0.6862879395484924},{"id":"https://openalex.org/keywords/positive-definite-matrix","display_name":"Positive-definite matrix","score":0.6050857305526733},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.594247043132782},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5756052732467651},{"id":"https://openalex.org/keywords/convex-function","display_name":"Convex function","score":0.52816241979599},{"id":"https://openalex.org/keywords/monotone-polygon","display_name":"Monotone polygon","score":0.48008185625076294},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.47341209650039673},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.46205204725265503},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.45752131938934326},{"id":"https://openalex.org/keywords/quadratic-function","display_name":"Quadratic function","score":0.4431104063987732},{"id":"https://openalex.org/keywords/quadratic-equation","display_name":"Quadratic equation","score":0.44138094782829285},{"id":"https://openalex.org/keywords/identity-matrix","display_name":"Identity matrix","score":0.436974436044693},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3859081268310547},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.3484942317008972},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.11003696918487549},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.09162107110023499},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.0743638277053833}],"concepts":[{"id":"https://openalex.org/C203616005","wikidata":"https://www.wikidata.org/wiki/Q620495","display_name":"Hessian matrix","level":2,"score":0.735491931438446},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6935430765151978},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.6862879395484924},{"id":"https://openalex.org/C49712288","wikidata":"https://www.wikidata.org/wiki/Q77601250","display_name":"Positive-definite matrix","level":3,"score":0.6050857305526733},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.594247043132782},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5756052732467651},{"id":"https://openalex.org/C145446738","wikidata":"https://www.wikidata.org/wiki/Q319913","display_name":"Convex function","level":3,"score":0.52816241979599},{"id":"https://openalex.org/C2834757","wikidata":"https://www.wikidata.org/wiki/Q4925424","display_name":"Monotone polygon","level":2,"score":0.48008185625076294},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.47341209650039673},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.46205204725265503},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.45752131938934326},{"id":"https://openalex.org/C166437778","wikidata":"https://www.wikidata.org/wiki/Q50695","display_name":"Quadratic function","level":3,"score":0.4431104063987732},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.44138094782829285},{"id":"https://openalex.org/C134567657","wikidata":"https://www.wikidata.org/wiki/Q193794","display_name":"Identity matrix","level":3,"score":0.436974436044693},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3859081268310547},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.3484942317008972},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.11003696918487549},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.09162107110023499},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0743638277053833},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0},{"id":"https://openalex.org/C127162648","wikidata":"https://www.wikidata.org/wiki/Q16858953","display_name":"Channel (broadcasting)","level":2,"score":0.0},{"id":"https://openalex.org/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","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},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"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/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1145/3449639.3459289","is_oa":true,"landing_page_url":"https://doi.org/10.1145/3449639.3459289","pdf_url":"https://dl.acm.org/action/downloadSupplement?doi=10.1145%2F3449639.3459289&file=p1169-morinaga.pdf","source":{"id":"https://openalex.org/S4363608932","display_name":"Proceedings of the Genetic and Evolutionary Computation Conference","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"conference"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the Genetic and Evolutionary Computation Conference","raw_type":"proceedings-article"}],"best_oa_location":{"id":"doi:10.1145/3449639.3459289","is_oa":true,"landing_page_url":"https://doi.org/10.1145/3449639.3459289","pdf_url":"https://dl.acm.org/action/downloadSupplement?doi=10.1145%2F3449639.3459289&file=p1169-morinaga.pdf","source":{"id":"https://openalex.org/S4363608932","display_name":"Proceedings of the Genetic and Evolutionary Computation Conference","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"conference"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the Genetic and Evolutionary Computation Conference","raw_type":"proceedings-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1069223013","display_name":null,"funder_award_id":"JSPS KAKENHI","funder_id":"https://openalex.org/F4320334764","funder_display_name":"Japan Society for the Promotion of Science"},{"id":"https://openalex.org/G3459562248","display_name":null,"funder_award_id":"Grant","funder_id":"https://openalex.org/F4320334764","funder_display_name":"Japan Society for the Promotion of Science"},{"id":"https://openalex.org/G3523681638","display_name":null,"funder_award_id":"19H04179","funder_id":"https://openalex.org/F4320334764","funder_display_name":"Japan Society for the Promotion of Science"},{"id":"https://openalex.org/G4227499671","display_name":null,"funder_award_id":"KAKENHI Grant","funder_id":"https://openalex.org/F4320334764","funder_display_name":"Japan Society for the Promotion of Science"},{"id":"https://openalex.org/G4636223006","display_name":null,"funder_award_id":"JSPS KAK","funder_id":"https://openalex.org/F4320334764","funder_display_name":"Japan Society for the Promotion of Science"},{"id":"https://openalex.org/G5786340949","display_name":null,"funder_award_id":"KAKENHI Grant Number","funder_id":"https://openalex.org/F4320334764","funder_display_name":"Japan Society for the Promotion of Science"},{"id":"https://openalex.org/G8430481527","display_name":null,"funder_award_id":"Number","funder_id":"https://openalex.org/F4320334764","funder_display_name":"Japan Society for the Promotion of Science"}],"funders":[{"id":"https://openalex.org/F4320334764","display_name":"Japan Society for the Promotion of Science","ror":"https://ror.org/00hhkn466"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3177118562.pdf","grobid_xml":"https://content.openalex.org/works/W3177118562.grobid-xml"},"referenced_works_count":28,"referenced_works":["https://openalex.org/W1523040298","https://openalex.org/W1559005923","https://openalex.org/W1971514372","https://openalex.org/W2023782941","https://openalex.org/W2027964569","https://openalex.org/W2030161963","https://openalex.org/W2068545576","https://openalex.org/W2106411386","https://openalex.org/W2112036188","https://openalex.org/W2121811374","https://openalex.org/W2135472208","https://openalex.org/W2138537392","https://openalex.org/W2140190473","https://openalex.org/W2149479912","https://openalex.org/W2160960847","https://openalex.org/W2168924884","https://openalex.org/W2492842172","https://openalex.org/W2783325233","https://openalex.org/W2888451463","https://openalex.org/W2914995607","https://openalex.org/W2946586661","https://openalex.org/W2951969141","https://openalex.org/W2953072278","https://openalex.org/W2962747045","https://openalex.org/W2963470657","https://openalex.org/W2964201809","https://openalex.org/W2969898098","https://openalex.org/W2972986629"],"related_works":["https://openalex.org/W3181458735","https://openalex.org/W4287079129","https://openalex.org/W3188860538","https://openalex.org/W2147587978","https://openalex.org/W2356931541","https://openalex.org/W2981801659","https://openalex.org/W2383807558","https://openalex.org/W2344249156","https://openalex.org/W164889054","https://openalex.org/W1579360376"],"abstract_inverted_index":{"The":[0,55],"(1+1)-evolution":[1],"strategy":[2],"(ES)":[3],"with":[4],"success-based":[5],"step-size":[6],"adaptation":[7],"is":[8,34,40,49,76,84,92,113,141,153],"analyzed":[9],"on":[10,158,178],"a":[11,35,41,67,159],"general":[12,160],"convex":[13,161],"quadratic":[14,162],"function":[15],"and":[16,45,90,120,156,181],"its":[17],"monotone":[18],"transformation,":[19],"that":[20,58],"is,":[21,59],"f(x)":[22],"=":[23,110,129],"g((x":[24],"-":[25,27],"x*)TH(x":[26],"x*)),":[28],"where":[29,82],"g:":[30],"R":[31,33],"\u2192":[32],"strictly":[36],"increasing":[37],"function,":[38,163],"H":[39,89,109,128,177],"positive-definite":[42],"symmetric":[43],"matrix,":[44],"x*":[46],"\u2208":[47],"Rd":[48],"the":[50,60,64,72,85,93,100,106,114,125,135,142,147,151,166,169,172,175,179,184,187],"optimal":[51,73],"solution":[52,74],"of":[53,63,88,95,103,108,117,127,137,150,168,171,186,190],"f.":[54],"convergence":[56,148],"rate,":[57],"decrease":[61],"rate":[62,102,149],"distance":[65],"from":[66],"search":[68],"point":[69],"mt":[70],"to":[71,78],"x*,":[75],"proven":[77],"be":[79],"in":[80,145,174],"O(exp(-L/Tr(H))),":[81],"L":[83],"smallest":[86],"eigenvalue":[87],"Tr(H)":[91],"trace":[94],"H.":[96,191],"This":[97],"result":[98],"generalizes":[99],"known":[101],"O(exp(-1/d))":[104],"for":[105,124],"case":[107,126],"Id":[111],"(Id":[112],"identity":[115],"matrix":[116],"dimension":[118],"d)":[119],"O(exp(-1/(d":[121],"\u00b7":[122,131],"\u03be)))":[123],"diag(\u03be":[130],"Id/2,":[132],"Id/2).":[133],"To":[134],"best":[136],"our":[138],"knowledge,":[139],"this":[140],"first":[143],"study":[144],"which":[146,164],"(1+1)-ES":[152],"derived":[154],"explicitly":[155],"rigorously":[157],"depicts":[165],"impact":[167,185],"distribution":[170],"eigenvalues":[173],"Hessian":[176],"optimization":[180],"not":[182],"only":[183],"condition":[188],"number":[189]},"counts_by_year":[{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":2}],"updated_date":"2026-03-07T16:01:11.037858","created_date":"2025-10-10T00:00:00"}