{"id":"https://openalex.org/W2943305848","doi":"https://doi.org/10.1007/s10208-021-09513-z","title":"A Theoretical and Empirical Comparison of Gradient Approximations in Derivative-Free Optimization","display_name":"A Theoretical and Empirical Comparison of Gradient Approximations in Derivative-Free Optimization","publication_year":2021,"publication_date":"2021-05-07","ids":{"openalex":"https://openalex.org/W2943305848","doi":"https://doi.org/10.1007/s10208-021-09513-z","mag":"2943305848"},"language":"en","primary_location":{"id":"doi:10.1007/s10208-021-09513-z","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10208-021-09513-z","pdf_url":null,"source":{"id":"https://openalex.org/S151639445","display_name":"Foundations of Computational Mathematics","issn_l":"1615-3375","issn":["1615-3375","1615-3383"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Foundations of Computational Mathematics","raw_type":"journal-article"},"type":"preprint","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1905.01332","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5029030164","display_name":"Albert S. Berahas","orcid":"https://orcid.org/0000-0002-2371-9398"},"institutions":[{"id":"https://openalex.org/I27837315","display_name":"University of Michigan\u2013Ann Arbor","ror":"https://ror.org/00jmfr291","country_code":"US","type":"education","lineage":["https://openalex.org/I27837315"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Albert S. Berahas","raw_affiliation_strings":["Department of Industrial and Operations Engineering, University of Michigan, Ann Arbor, MI, USA","[Department of Industrial and Operations Engineering, University of Michigan, Ann Arbor, USA]"],"affiliations":[{"raw_affiliation_string":"Department of Industrial and Operations Engineering, University of Michigan, Ann Arbor, MI, USA","institution_ids":["https://openalex.org/I27837315"]},{"raw_affiliation_string":"[Department of Industrial and Operations Engineering, University of Michigan, Ann Arbor, USA]","institution_ids":["https://openalex.org/I27837315"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5019637134","display_name":"Liyuan Cao","orcid":"https://orcid.org/0000-0001-5146-783X"},"institutions":[{"id":"https://openalex.org/I186143895","display_name":"Lehigh University","ror":"https://ror.org/012afjb06","country_code":"US","type":"education","lineage":["https://openalex.org/I186143895"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Liyuan Cao","raw_affiliation_strings":["Department of Industrial and Systems Engineering, Lehigh University, Bethlehem, PA, USA","Dept. of Industrial & Systems Engineering, Lehigh University, Bethlehem, USA"],"affiliations":[{"raw_affiliation_string":"Department of Industrial and Systems Engineering, Lehigh University, Bethlehem, PA, USA","institution_ids":["https://openalex.org/I186143895"]},{"raw_affiliation_string":"Dept. of Industrial & Systems Engineering, Lehigh University, Bethlehem, USA","institution_ids":["https://openalex.org/I186143895"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5031842812","display_name":"Krzysztof Choroma\u0144ski","orcid":"https://orcid.org/0000-0003-3626-414X"},"institutions":[{"id":"https://openalex.org/I1291425158","display_name":"Google (United States)","ror":"https://ror.org/00njsd438","country_code":"US","type":"company","lineage":["https://openalex.org/I1291425158","https://openalex.org/I4210128969"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Krzysztof Choromanski","raw_affiliation_strings":["Google Brain, New York, NY, USA","Google Brain, New York, USA"],"affiliations":[{"raw_affiliation_string":"Google Brain, New York, NY, USA","institution_ids":["https://openalex.org/I1291425158"]},{"raw_affiliation_string":"Google Brain, New York, USA","institution_ids":["https://openalex.org/I1291425158"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5026789944","display_name":"Katya Scheinberg","orcid":"https://orcid.org/0000-0003-3547-1841"},"institutions":[{"id":"https://openalex.org/I205783295","display_name":"Cornell University","ror":"https://ror.org/05bnh6r87","country_code":"US","type":"education","lineage":["https://openalex.org/I205783295"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Katya Scheinberg","raw_affiliation_strings":["Department of Operations Research and Information Engineering, Cornell University, Ithaca, NY, USA","Department of Operations Research and Information Engineering, Cornell University, Ithaca, USA#TAB#"],"affiliations":[{"raw_affiliation_string":"Department of Operations Research and Information Engineering, Cornell University, Ithaca, NY, USA","institution_ids":["https://openalex.org/I205783295"]},{"raw_affiliation_string":"Department of Operations Research and Information Engineering, Cornell University, Ithaca, USA#TAB#","institution_ids":["https://openalex.org/I205783295"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5029030164"],"corresponding_institution_ids":["https://openalex.org/I27837315"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":null,"fwci":6.8383,"has_fulltext":true,"cited_by_count":39,"citation_normalized_percentile":{"value":0.97890485,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":91,"max":99},"biblio":{"volume":"22","issue":"2","first_page":"507","last_page":"560"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9998000264167786,"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"}},"topics":[{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9998000264167786,"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/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9997000098228455,"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/T11612","display_name":"Stochastic Gradient Optimization Techniques","score":0.9994000196456909,"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/smoothing","display_name":"Smoothing","score":0.8098970651626587},{"id":"https://openalex.org/keywords/line-search","display_name":"Line search","score":0.7728807330131531},{"id":"https://openalex.org/keywords/interpolation","display_name":"Interpolation (computer graphics)","score":0.616493284702301},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6144771575927734},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5958465337753296},{"id":"https://openalex.org/keywords/gaussian","display_name":"Gaussian","score":0.5787609219551086},{"id":"https://openalex.org/keywords/gradient-descent","display_name":"Gradient descent","score":0.5220165848731995},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5199040770530701},{"id":"https://openalex.org/keywords/gaussian-blur","display_name":"Gaussian blur","score":0.4896445870399475},{"id":"https://openalex.org/keywords/derivative-free-optimization","display_name":"Derivative-free optimization","score":0.4573501944541931},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.45124009251594543},{"id":"https://openalex.org/keywords/derivative","display_name":"Derivative (finance)","score":0.4352577030658722},{"id":"https://openalex.org/keywords/descent-direction","display_name":"Descent direction","score":0.42809003591537476},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.426923006772995},{"id":"https://openalex.org/keywords/line","display_name":"Line (geometry)","score":0.4267820715904236},{"id":"https://openalex.org/keywords/optimization-problem","display_name":"Optimization problem","score":0.34119826555252075},{"id":"https://openalex.org/keywords/radius","display_name":"RADIUS","score":0.23791658878326416},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.23329481482505798},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.07408306002616882},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.07218420505523682}],"concepts":[{"id":"https://openalex.org/C3770464","wikidata":"https://www.wikidata.org/wiki/Q775963","display_name":"Smoothing","level":2,"score":0.8098970651626587},{"id":"https://openalex.org/C85522705","wikidata":"https://www.wikidata.org/wiki/Q3278015","display_name":"Line search","level":3,"score":0.7728807330131531},{"id":"https://openalex.org/C137800194","wikidata":"https://www.wikidata.org/wiki/Q11713455","display_name":"Interpolation (computer graphics)","level":3,"score":0.616493284702301},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6144771575927734},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5958465337753296},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.5787609219551086},{"id":"https://openalex.org/C153258448","wikidata":"https://www.wikidata.org/wiki/Q1199743","display_name":"Gradient descent","level":3,"score":0.5220165848731995},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5199040770530701},{"id":"https://openalex.org/C104317376","wikidata":"https://www.wikidata.org/wiki/Q1894545","display_name":"Gaussian blur","level":5,"score":0.4896445870399475},{"id":"https://openalex.org/C29282572","wikidata":"https://www.wikidata.org/wiki/Q16977029","display_name":"Derivative-free optimization","level":4,"score":0.4573501944541931},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.45124009251594543},{"id":"https://openalex.org/C111771559","wikidata":"https://www.wikidata.org/wiki/Q66295","display_name":"Derivative (finance)","level":2,"score":0.4352577030658722},{"id":"https://openalex.org/C116149140","wikidata":"https://www.wikidata.org/wiki/Q2070951","display_name":"Descent direction","level":4,"score":0.42809003591537476},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.426923006772995},{"id":"https://openalex.org/C198352243","wikidata":"https://www.wikidata.org/wiki/Q37105","display_name":"Line (geometry)","level":2,"score":0.4267820715904236},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.34119826555252075},{"id":"https://openalex.org/C178635117","wikidata":"https://www.wikidata.org/wiki/Q747499","display_name":"RADIUS","level":2,"score":0.23791658878326416},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.23329481482505798},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.07408306002616882},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.07218420505523682},{"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/C106159729","wikidata":"https://www.wikidata.org/wiki/Q2294553","display_name":"Financial economics","level":1,"score":0.0},{"id":"https://openalex.org/C121684516","wikidata":"https://www.wikidata.org/wiki/Q7600677","display_name":"Computer graphics (images)","level":1,"score":0.0},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","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/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.0},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","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},{"id":"https://openalex.org/C106430172","wikidata":"https://www.wikidata.org/wiki/Q6002272","display_name":"Image restoration","level":4,"score":0.0},{"id":"https://openalex.org/C9417928","wikidata":"https://www.wikidata.org/wiki/Q1070689","display_name":"Image processing","level":3,"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/C122357587","wikidata":"https://www.wikidata.org/wiki/Q6934508","display_name":"Multi-swarm optimization","level":3,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C502989409","wikidata":"https://www.wikidata.org/wiki/Q11425","display_name":"Animation","level":2,"score":0.0},{"id":"https://openalex.org/C115961682","wikidata":"https://www.wikidata.org/wiki/Q860623","display_name":"Image (mathematics)","level":2,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1007/s10208-021-09513-z","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10208-021-09513-z","pdf_url":null,"source":{"id":"https://openalex.org/S151639445","display_name":"Foundations of Computational Mathematics","issn_l":"1615-3375","issn":["1615-3375","1615-3383"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Foundations of Computational Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1905.01332","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1905.01332","pdf_url":"https://arxiv.org/pdf/1905.01332","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"mag:2943305848","is_oa":true,"landing_page_url":"http://export.arxiv.org/pdf/1905.01332","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},{"id":"doi:10.48550/arxiv.1905.01332","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1905.01332","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1905.01332","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1905.01332","pdf_url":"https://arxiv.org/pdf/1905.01332","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2943305848.pdf","grobid_xml":"https://content.openalex.org/works/W2943305848.grobid-xml"},"referenced_works_count":52,"referenced_works":["https://openalex.org/W72823879","https://openalex.org/W181733065","https://openalex.org/W1568288633","https://openalex.org/W1748199557","https://openalex.org/W1771410628","https://openalex.org/W2004001705","https://openalex.org/W2009797711","https://openalex.org/W2030874933","https://openalex.org/W2052143039","https://openalex.org/W2055762706","https://openalex.org/W2057830724","https://openalex.org/W2060279602","https://openalex.org/W2061570747","https://openalex.org/W2064076655","https://openalex.org/W2071436527","https://openalex.org/W2077667520","https://openalex.org/W2078950386","https://openalex.org/W2106120648","https://openalex.org/W2112449769","https://openalex.org/W2137633966","https://openalex.org/W2149454052","https://openalex.org/W2149479912","https://openalex.org/W2151965738","https://openalex.org/W2161149069","https://openalex.org/W2171830216","https://openalex.org/W2290899512","https://openalex.org/W2565654137","https://openalex.org/W2579825744","https://openalex.org/W2596367596","https://openalex.org/W2605076685","https://openalex.org/W2767380555","https://openalex.org/W2783919261","https://openalex.org/W2796248693","https://openalex.org/W2796416676","https://openalex.org/W2886474253","https://openalex.org/W2891563122","https://openalex.org/W2902020649","https://openalex.org/W2941034199","https://openalex.org/W2962876518","https://openalex.org/W2963030777","https://openalex.org/W2963184463","https://openalex.org/W2963243330","https://openalex.org/W2963308146","https://openalex.org/W2963470657","https://openalex.org/W2963477800","https://openalex.org/W2963480953","https://openalex.org/W2964089577","https://openalex.org/W2982647371","https://openalex.org/W3005484777","https://openalex.org/W3102143361","https://openalex.org/W3173141421","https://openalex.org/W4211042066"],"related_works":["https://openalex.org/W2149479912","https://openalex.org/W3102143361","https://openalex.org/W181733065","https://openalex.org/W2596367596","https://openalex.org/W2004001705","https://openalex.org/W2963470657","https://openalex.org/W2605076685","https://openalex.org/W2171830216","https://openalex.org/W2171074980","https://openalex.org/W2963477800","https://openalex.org/W2029463628","https://openalex.org/W3029645440","https://openalex.org/W2979411530","https://openalex.org/W2160960847","https://openalex.org/W2886474253","https://openalex.org/W2137633966","https://openalex.org/W2112036188","https://openalex.org/W2963308146","https://openalex.org/W2963243330","https://openalex.org/W2052143039"],"abstract_inverted_index":null,"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2022,"cited_by_count":7},{"year":2021,"cited_by_count":13},{"year":2020,"cited_by_count":13},{"year":2019,"cited_by_count":3}],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2025-10-10T00:00:00"}
