{"id":"https://openalex.org/W2087164501","doi":"https://doi.org/10.1137/120891216","title":"On Directional Metric Subregularity and Second-Order Optimality Conditions for a Class of Nonsmooth Mathematical Programs","display_name":"On Directional Metric Subregularity and Second-Order Optimality Conditions for a Class of Nonsmooth Mathematical Programs","publication_year":2013,"publication_date":"2013-01-01","ids":{"openalex":"https://openalex.org/W2087164501","doi":"https://doi.org/10.1137/120891216","mag":"2087164501"},"language":"en","primary_location":{"id":"doi:10.1137/120891216","is_oa":false,"landing_page_url":"https://doi.org/10.1137/120891216","pdf_url":null,"source":{"id":"https://openalex.org/S928796702","display_name":"SIAM Journal on Optimization","issn_l":"1052-6234","issn":["1052-6234","1095-7189"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Optimization","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/A5039711962","display_name":"Helmut Gfrerer","orcid":"https://orcid.org/0000-0001-6860-102X"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Helmut Gfrerer","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5039711962"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":4.3505,"has_fulltext":false,"cited_by_count":61,"citation_normalized_percentile":{"value":0.94624331,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"23","issue":"1","first_page":"632","last_page":"665"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10545","display_name":"Optimization and Variational Analysis","score":0.9998999834060669,"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"}},"topics":[{"id":"https://openalex.org/T10545","display_name":"Optimization and Variational Analysis","score":0.9998999834060669,"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"}},{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9901999831199646,"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/T11115","display_name":"Topology Optimization in Engineering","score":0.9843999743461609,"subfield":{"id":"https://openalex.org/subfields/2205","display_name":"Civil and Structural Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8246204853057861},{"id":"https://openalex.org/keywords/metric","display_name":"Metric (unit)","score":0.6517618894577026},{"id":"https://openalex.org/keywords/constraint","display_name":"Constraint (computer-aided design)","score":0.6449657678604126},{"id":"https://openalex.org/keywords/variational-analysis","display_name":"Variational analysis","score":0.6127879023551941},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5552161931991577},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.5502066612243652},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.5399179458618164},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.4605424106121063},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.45610859990119934},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.42021802067756653},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4014705419540405},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.1468823254108429},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.12993255257606506}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8246204853057861},{"id":"https://openalex.org/C176217482","wikidata":"https://www.wikidata.org/wiki/Q860554","display_name":"Metric (unit)","level":2,"score":0.6517618894577026},{"id":"https://openalex.org/C2776036281","wikidata":"https://www.wikidata.org/wiki/Q48769818","display_name":"Constraint (computer-aided design)","level":2,"score":0.6449657678604126},{"id":"https://openalex.org/C523394659","wikidata":"https://www.wikidata.org/wiki/Q17086892","display_name":"Variational analysis","level":2,"score":0.6127879023551941},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5552161931991577},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.5502066612243652},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.5399179458618164},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.4605424106121063},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.45610859990119934},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.42021802067756653},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4014705419540405},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.1468823254108429},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.12993255257606506},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"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/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","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/C21547014","wikidata":"https://www.wikidata.org/wiki/Q1423657","display_name":"Operations management","level":1,"score":0.0},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/120891216","is_oa":false,"landing_page_url":"https://doi.org/10.1137/120891216","pdf_url":null,"source":{"id":"https://openalex.org/S928796702","display_name":"SIAM Journal on Optimization","issn_l":"1052-6234","issn":["1052-6234","1095-7189"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Optimization","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":27,"referenced_works":["https://openalex.org/W583272553","https://openalex.org/W651290840","https://openalex.org/W1583089965","https://openalex.org/W1601741115","https://openalex.org/W1991203806","https://openalex.org/W1994724562","https://openalex.org/W2002371412","https://openalex.org/W2014715559","https://openalex.org/W2020150158","https://openalex.org/W2021639918","https://openalex.org/W2033316062","https://openalex.org/W2042153418","https://openalex.org/W2069369032","https://openalex.org/W2073311565","https://openalex.org/W2079852585","https://openalex.org/W2081704372","https://openalex.org/W2086592650","https://openalex.org/W2116407586","https://openalex.org/W2118434696","https://openalex.org/W2129779377","https://openalex.org/W2130182197","https://openalex.org/W2131815933","https://openalex.org/W2141642552","https://openalex.org/W2150140216","https://openalex.org/W2153565720","https://openalex.org/W2334285086","https://openalex.org/W3157341860"],"related_works":["https://openalex.org/W2807251790","https://openalex.org/W2799406489","https://openalex.org/W2049792449","https://openalex.org/W986251431","https://openalex.org/W2503798035","https://openalex.org/W2959160600","https://openalex.org/W563727013","https://openalex.org/W2502468346","https://openalex.org/W2963420405","https://openalex.org/W2519041334"],"abstract_inverted_index":{"We":[0],"study":[1],"infinite":[2],"dimensional":[3],"optimization":[4,70],"problems":[5],"where":[6],"the":[7,13,25,56,69],"constraint":[8,57],"mapping":[9,28],"is":[10],"given":[11],"as":[12],"sum":[14],"of":[15,29,38,55],"a":[16,20,30],"smooth":[17],"function":[18],"and":[19,44,49],"generalized":[21],"polyhedral":[22,32],"multifunction,":[23],"e.g.,":[24],"normal":[26],"cone":[27],"convex":[31],"set.":[33],"By":[34],"using":[35],"advanced":[36],"techniques":[37],"variational":[39],"analysis":[40],"we":[41],"obtain":[42,64],"first-order":[43],"second-order":[45,65],"characterizations,":[46],"both":[47],"necessary":[48],"sufficient,":[50],"for":[51,68],"directional":[52],"metric":[53],"subregularity":[54],"mapping.":[58],"These":[59],"results":[60],"are":[61],"used":[62],"to":[63],"optimality":[66],"conditions":[67],"problem.":[71]},"counts_by_year":[{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":6},{"year":2020,"cited_by_count":5},{"year":2019,"cited_by_count":12},{"year":2018,"cited_by_count":6},{"year":2017,"cited_by_count":9},{"year":2016,"cited_by_count":5},{"year":2015,"cited_by_count":4},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}