{"id":"https://openalex.org/W188839581","doi":"https://doi.org/10.1007/bf02243624","title":"Numerically stable computation of step-sizes for descent methods. The nonconvex case","display_name":"Numerically stable computation of step-sizes for descent methods. The nonconvex case","publication_year":1977,"publication_date":"1977-06-01","ids":{"openalex":"https://openalex.org/W188839581","doi":"https://doi.org/10.1007/bf02243624","mag":"188839581"},"language":"en","primary_location":{"id":"doi:10.1007/bf02243624","is_oa":false,"landing_page_url":"https://doi.org/10.1007/bf02243624","pdf_url":null,"source":{"id":"https://openalex.org/S35593046","display_name":"Computing","issn_l":"0010-485X","issn":["0010-485X","1436-5057"],"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":"Computing","raw_type":"journal-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/A5071285666","display_name":"Peter Spellucci","orcid":null},"institutions":[{"id":"https://openalex.org/I197323543","display_name":"Johannes Gutenberg University Mainz","ror":"https://ror.org/023b0x485","country_code":"DE","type":"education","lineage":["https://openalex.org/I197323543"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"P. Spellucci","raw_affiliation_strings":["Fachbereich Mathematik, Johannes-Gutenberg-Universit\u00e4t, Postfach 3980, D-6500, Mainz, Federal Republic of Germany","Fachbereich Mathematik, Johannes Gutenberg-Universit\u00e4t, Mainz, Federal Republic of Germany"],"affiliations":[{"raw_affiliation_string":"Fachbereich Mathematik, Johannes-Gutenberg-Universit\u00e4t, Postfach 3980, D-6500, Mainz, Federal Republic of Germany","institution_ids":["https://openalex.org/I197323543"]},{"raw_affiliation_string":"Fachbereich Mathematik, Johannes Gutenberg-Universit\u00e4t, Mainz, Federal Republic of Germany","institution_ids":["https://openalex.org/I197323543"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5071285666"],"corresponding_institution_ids":["https://openalex.org/I197323543"],"apc_list":{"value":2290,"currency":"EUR","value_usd":2890},"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.02246321,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"18","issue":"2","first_page":"149","last_page":"160"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9997000098228455,"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":0.9997000098228455,"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/T11205","display_name":"Numerical methods in inverse problems","score":0.9983999729156494,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/T10545","display_name":"Optimization and Variational Analysis","score":0.995199978351593,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"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/computation","display_name":"Computation","score":0.7804862260818481},{"id":"https://openalex.org/keywords/range","display_name":"Range (aeronautics)","score":0.6530634164810181},{"id":"https://openalex.org/keywords/descent","display_name":"Descent (aeronautics)","score":0.6523041129112244},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6402097940444946},{"id":"https://openalex.org/keywords/gradient-descent","display_name":"Gradient descent","score":0.5996245741844177},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.5900622010231018},{"id":"https://openalex.org/keywords/minification","display_name":"Minification","score":0.5876667499542236},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.518552839756012},{"id":"https://openalex.org/keywords/convex-function","display_name":"Convex function","score":0.4888984262943268},{"id":"https://openalex.org/keywords/descent-direction","display_name":"Descent direction","score":0.47165361046791077},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.47085922956466675},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.4668007493019104},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.45356839895248413},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.418062686920166},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3317541480064392},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.07237622141838074},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.052757978439331055}],"concepts":[{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.7804862260818481},{"id":"https://openalex.org/C204323151","wikidata":"https://www.wikidata.org/wiki/Q905424","display_name":"Range (aeronautics)","level":2,"score":0.6530634164810181},{"id":"https://openalex.org/C2776637919","wikidata":"https://www.wikidata.org/wiki/Q624380","display_name":"Descent (aeronautics)","level":2,"score":0.6523041129112244},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6402097940444946},{"id":"https://openalex.org/C153258448","wikidata":"https://www.wikidata.org/wiki/Q1199743","display_name":"Gradient descent","level":3,"score":0.5996245741844177},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5900622010231018},{"id":"https://openalex.org/C147764199","wikidata":"https://www.wikidata.org/wiki/Q6865248","display_name":"Minification","level":2,"score":0.5876667499542236},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.518552839756012},{"id":"https://openalex.org/C145446738","wikidata":"https://www.wikidata.org/wiki/Q319913","display_name":"Convex function","level":3,"score":0.4888984262943268},{"id":"https://openalex.org/C116149140","wikidata":"https://www.wikidata.org/wiki/Q2070951","display_name":"Descent direction","level":4,"score":0.47165361046791077},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.47085922956466675},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.4668007493019104},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.45356839895248413},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.418062686920166},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3317541480064392},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.07237622141838074},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.052757978439331055},{"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/C146978453","wikidata":"https://www.wikidata.org/wiki/Q3798668","display_name":"Aerospace engineering","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/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"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/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"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/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/bf02243624","is_oa":false,"landing_page_url":"https://doi.org/10.1007/bf02243624","pdf_url":null,"source":{"id":"https://openalex.org/S35593046","display_name":"Computing","issn_l":"0010-485X","issn":["0010-485X","1436-5057"],"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":"Computing","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Reduced inequalities","id":"https://metadata.un.org/sdg/10","score":0.47999998927116394}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":12,"referenced_works":["https://openalex.org/W46774698","https://openalex.org/W199990928","https://openalex.org/W1600159612","https://openalex.org/W1964712205","https://openalex.org/W1969811075","https://openalex.org/W1973110562","https://openalex.org/W1988849934","https://openalex.org/W2078950386","https://openalex.org/W2090963365","https://openalex.org/W2112469048","https://openalex.org/W2598222462","https://openalex.org/W4299512035"],"related_works":["https://openalex.org/W2015288657","https://openalex.org/W39176023","https://openalex.org/W1985812215","https://openalex.org/W2098072525","https://openalex.org/W9059077","https://openalex.org/W2111200844","https://openalex.org/W4297883503","https://openalex.org/W4389767465","https://openalex.org/W2054621035","https://openalex.org/W4313177131"],"abstract_inverted_index":null,"counts_by_year":[{"year":2012,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}