{"id":"https://openalex.org/W2037676515","doi":"https://doi.org/10.1007/s10107-006-0007-2","title":"Error Bounds of Regularized Gap Functions for Nonsmooth Variational Inequality Problems","display_name":"Error Bounds of Regularized Gap Functions for Nonsmooth Variational Inequality Problems","publication_year":2006,"publication_date":"2006-06-21","ids":{"openalex":"https://openalex.org/W2037676515","doi":"https://doi.org/10.1007/s10107-006-0007-2","mag":"2037676515"},"language":"en","primary_location":{"id":"doi:10.1007/s10107-006-0007-2","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10107-006-0007-2","pdf_url":null,"source":{"id":"https://openalex.org/S193920097","display_name":"Mathematical Programming","issn_l":"0025-5610","issn":["0025-5610","1436-4646"],"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":"Mathematical Programming","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/A5014862456","display_name":"Kung Fu Ng","orcid":null},"institutions":[{"id":"https://openalex.org/I177725633","display_name":"Chinese University of Hong Kong","ror":"https://ror.org/00t33hh48","country_code":"CN","type":"education","lineage":["https://openalex.org/I177725633"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Kung Fu Ng","raw_affiliation_strings":["Department of Mathematics, The Chinese University of Hong Kong, Hong Kong, People\u2019s Republic of China","The Chinese University of Hong Kong, Department of Mathematics, Hong Kong, People\u2019s Republic of China#TAB#"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, The Chinese University of Hong Kong, Hong Kong, People\u2019s Republic of China","institution_ids":["https://openalex.org/I177725633"]},{"raw_affiliation_string":"The Chinese University of Hong Kong, Department of Mathematics, Hong Kong, People\u2019s Republic of China#TAB#","institution_ids":["https://openalex.org/I177725633"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5055959154","display_name":"Lu Tan","orcid":"https://orcid.org/0000-0002-3361-3060"},"institutions":[{"id":"https://openalex.org/I177725633","display_name":"Chinese University of Hong Kong","ror":"https://ror.org/00t33hh48","country_code":"CN","type":"education","lineage":["https://openalex.org/I177725633"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Lu Lin Tan","raw_affiliation_strings":["Department of Mathematics, The Chinese University of Hong Kong, Hong Kong, People\u2019s Republic of China","The Chinese University of Hong Kong, Department of Mathematics, Hong Kong, People\u2019s Republic of China#TAB#"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, The Chinese University of Hong Kong, Hong Kong, People\u2019s Republic of China","institution_ids":["https://openalex.org/I177725633"]},{"raw_affiliation_string":"The Chinese University of Hong Kong, Department of Mathematics, Hong Kong, People\u2019s Republic of China#TAB#","institution_ids":["https://openalex.org/I177725633"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5014862456"],"corresponding_institution_ids":["https://openalex.org/I177725633"],"apc_list":{"value":2190,"currency":"EUR","value_usd":2890},"apc_paid":null,"fwci":1.6902,"has_fulltext":false,"cited_by_count":23,"citation_normalized_percentile":{"value":0.83778106,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"110","issue":"2","first_page":"405","last_page":"429"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10545","display_name":"Optimization and Variational Analysis","score":0.9995999932289124,"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":0.9995999932289124,"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/T12809","display_name":"Contact Mechanics and Variational Inequalities","score":0.9980000257492065,"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/T11115","display_name":"Topology Optimization in Engineering","score":0.9886000156402588,"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":0.8986600637435913},{"id":"https://openalex.org/keywords/differentiable-function","display_name":"Differentiable function","score":0.7465223073959351},{"id":"https://openalex.org/keywords/monotonic-function","display_name":"Monotonic function","score":0.7137539386749268},{"id":"https://openalex.org/keywords/lipschitz-continuity","display_name":"Lipschitz continuity","score":0.6900161504745483},{"id":"https://openalex.org/keywords/variational-inequality","display_name":"Variational inequality","score":0.5960984230041504},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.48889198899269104},{"id":"https://openalex.org/keywords/convex-function","display_name":"Convex function","score":0.4819178879261017},{"id":"https://openalex.org/keywords/euclidean-space","display_name":"Euclidean space","score":0.45816144347190857},{"id":"https://openalex.org/keywords/euclidean-geometry","display_name":"Euclidean geometry","score":0.45323798060417175},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.44670355319976807},{"id":"https://openalex.org/keywords/subderivative","display_name":"Subderivative","score":0.42913079261779785},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.39154839515686035},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.36430615186691284},{"id":"https://openalex.org/keywords/convex-optimization","display_name":"Convex optimization","score":0.25500887632369995}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8986600637435913},{"id":"https://openalex.org/C202615002","wikidata":"https://www.wikidata.org/wiki/Q783507","display_name":"Differentiable function","level":2,"score":0.7465223073959351},{"id":"https://openalex.org/C72169020","wikidata":"https://www.wikidata.org/wiki/Q194404","display_name":"Monotonic function","level":2,"score":0.7137539386749268},{"id":"https://openalex.org/C22324862","wikidata":"https://www.wikidata.org/wiki/Q652707","display_name":"Lipschitz continuity","level":2,"score":0.6900161504745483},{"id":"https://openalex.org/C161999928","wikidata":"https://www.wikidata.org/wiki/Q4556320","display_name":"Variational inequality","level":2,"score":0.5960984230041504},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.48889198899269104},{"id":"https://openalex.org/C145446738","wikidata":"https://www.wikidata.org/wiki/Q319913","display_name":"Convex function","level":3,"score":0.4819178879261017},{"id":"https://openalex.org/C186450821","wikidata":"https://www.wikidata.org/wiki/Q17295","display_name":"Euclidean space","level":2,"score":0.45816144347190857},{"id":"https://openalex.org/C129782007","wikidata":"https://www.wikidata.org/wiki/Q162886","display_name":"Euclidean geometry","level":2,"score":0.45323798060417175},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.44670355319976807},{"id":"https://openalex.org/C200661725","wikidata":"https://www.wikidata.org/wiki/Q289500","display_name":"Subderivative","level":4,"score":0.42913079261779785},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.39154839515686035},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.36430615186691284},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.25500887632369995},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"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/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s10107-006-0007-2","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10107-006-0007-2","pdf_url":null,"source":{"id":"https://openalex.org/S193920097","display_name":"Mathematical Programming","issn_l":"0025-5610","issn":["0025-5610","1436-4646"],"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":"Mathematical Programming","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/10","display_name":"Reduced inequalities","score":0.7300000190734863}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":30,"referenced_works":["https://openalex.org/W852774244","https://openalex.org/W1518078339","https://openalex.org/W1551360398","https://openalex.org/W1948466936","https://openalex.org/W1970441758","https://openalex.org/W1985348591","https://openalex.org/W1994091857","https://openalex.org/W2001598548","https://openalex.org/W2016401302","https://openalex.org/W2029032225","https://openalex.org/W2043032734","https://openalex.org/W2054049854","https://openalex.org/W2061750102","https://openalex.org/W2065121429","https://openalex.org/W2071878201","https://openalex.org/W2076736386","https://openalex.org/W2076982017","https://openalex.org/W2083030901","https://openalex.org/W2093246563","https://openalex.org/W2097273628","https://openalex.org/W2110041091","https://openalex.org/W2114605231","https://openalex.org/W2171587393","https://openalex.org/W2482182218","https://openalex.org/W2971350920","https://openalex.org/W4212988175","https://openalex.org/W4213260966","https://openalex.org/W4236123449","https://openalex.org/W4241481124","https://openalex.org/W4249513058"],"related_works":["https://openalex.org/W3185235544","https://openalex.org/W2897842840","https://openalex.org/W2911623553","https://openalex.org/W4297791327","https://openalex.org/W2397777611","https://openalex.org/W2072255091","https://openalex.org/W2761731838","https://openalex.org/W4221091651","https://openalex.org/W2084754442","https://openalex.org/W2356958610"],"abstract_inverted_index":null,"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":1},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":3},{"year":2014,"cited_by_count":3},{"year":2013,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
