{"id":"https://openalex.org/W3199316543","doi":"https://doi.org/10.1007/s10589-021-00316-0","title":"$${\\text {B}}$$-subdifferentials of the projection onto the matrix simplex","display_name":"$${\\text {B}}$$-subdifferentials of the projection onto the matrix simplex","publication_year":2021,"publication_date":"2021-09-20","ids":{"openalex":"https://openalex.org/W3199316543","doi":"https://doi.org/10.1007/s10589-021-00316-0","mag":"3199316543"},"language":"en","primary_location":{"id":"doi:10.1007/s10589-021-00316-0","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10589-021-00316-0","pdf_url":null,"source":{"id":"https://openalex.org/S39243548","display_name":"Computational Optimization and Applications","issn_l":"0926-6003","issn":["0926-6003","1573-2894"],"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":"Computational Optimization and Applications","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/A5034991793","display_name":"Shenglong Hu","orcid":"https://orcid.org/0000-0003-0036-2880"},"institutions":[{"id":"https://openalex.org/I50760025","display_name":"Hangzhou Dianzi University","ror":"https://ror.org/0576gt767","country_code":"CN","type":"education","lineage":["https://openalex.org/I50760025"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Shenglong Hu","raw_affiliation_strings":["Department of Mathematics, School of Science, Hangzhou Dianzi University, Hangzhou, 310018, China","Department of Mathematics, School of Science, Hangzhou Dianzi University, Hangzhou, China"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, School of Science, Hangzhou Dianzi University, Hangzhou, 310018, China","institution_ids":["https://openalex.org/I50760025"]},{"raw_affiliation_string":"Department of Mathematics, School of Science, Hangzhou Dianzi University, Hangzhou, China","institution_ids":["https://openalex.org/I50760025"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5025579166","display_name":"Guoyin Li","orcid":"https://orcid.org/0000-0002-2099-7974"},"institutions":[{"id":"https://openalex.org/I31746571","display_name":"UNSW Sydney","ror":"https://ror.org/03r8z3t63","country_code":"AU","type":"education","lineage":["https://openalex.org/I31746571"]}],"countries":["AU"],"is_corresponding":false,"raw_author_name":"Guoyin Li","raw_affiliation_strings":["Department of Applied Mathematics, University of New South Wales, Sydney, 2052, Australia","Department of Applied Mathematics, University of New South Wales, Sydney, Australia"],"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics, University of New South Wales, Sydney, 2052, Australia","institution_ids":["https://openalex.org/I31746571"]},{"raw_affiliation_string":"Department of Applied Mathematics, University of New South Wales, Sydney, Australia","institution_ids":["https://openalex.org/I31746571"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5034991793"],"corresponding_institution_ids":["https://openalex.org/I50760025"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":null,"fwci":0.4522,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.68344997,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"80","issue":"3","first_page":"915","last_page":"941"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","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/T10792","display_name":"Matrix Theory and Algorithms","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":0.9998000264167786,"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":0.9968000054359436,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7632001638412476},{"id":"https://openalex.org/keywords/simplex","display_name":"Simplex","score":0.7442346811294556},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.6392125487327576},{"id":"https://openalex.org/keywords/semidefinite-programming","display_name":"Semidefinite programming","score":0.6255131363868713},{"id":"https://openalex.org/keywords/projection","display_name":"Projection (relational algebra)","score":0.5877573490142822},{"id":"https://openalex.org/keywords/positive-definite-matrix","display_name":"Positive-definite matrix","score":0.528462827205658},{"id":"https://openalex.org/keywords/symmetric-matrix","display_name":"Symmetric matrix","score":0.48538267612457275},{"id":"https://openalex.org/keywords/cone","display_name":"Cone (formal languages)","score":0.477251261472702},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.4556972086429596},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.4426092207431793},{"id":"https://openalex.org/keywords/conic-optimization","display_name":"Conic optimization","score":0.4304533898830414},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.38159939646720886},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.35762208700180054},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3492123484611511},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3005434572696686},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.28581541776657104},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.26356756687164307},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.16535788774490356},{"id":"https://openalex.org/keywords/convex-optimization","display_name":"Convex optimization","score":0.15452119708061218},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.09409049153327942},{"id":"https://openalex.org/keywords/convex-set","display_name":"Convex set","score":0.08688858151435852},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.07868942618370056}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7632001638412476},{"id":"https://openalex.org/C62438384","wikidata":"https://www.wikidata.org/wiki/Q331350","display_name":"Simplex","level":2,"score":0.7442346811294556},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.6392125487327576},{"id":"https://openalex.org/C101901036","wikidata":"https://www.wikidata.org/wiki/Q2269096","display_name":"Semidefinite programming","level":2,"score":0.6255131363868713},{"id":"https://openalex.org/C57493831","wikidata":"https://www.wikidata.org/wiki/Q3134666","display_name":"Projection (relational algebra)","level":2,"score":0.5877573490142822},{"id":"https://openalex.org/C49712288","wikidata":"https://www.wikidata.org/wiki/Q77601250","display_name":"Positive-definite matrix","level":3,"score":0.528462827205658},{"id":"https://openalex.org/C54848796","wikidata":"https://www.wikidata.org/wiki/Q339011","display_name":"Symmetric matrix","level":3,"score":0.48538267612457275},{"id":"https://openalex.org/C30014739","wikidata":"https://www.wikidata.org/wiki/Q5159445","display_name":"Cone (formal languages)","level":2,"score":0.477251261472702},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4556972086429596},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.4426092207431793},{"id":"https://openalex.org/C79187972","wikidata":"https://www.wikidata.org/wiki/Q2654791","display_name":"Conic optimization","level":5,"score":0.4304533898830414},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.38159939646720886},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.35762208700180054},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3492123484611511},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3005434572696686},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.28581541776657104},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.26356756687164307},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.16535788774490356},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.15452119708061218},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.09409049153327942},{"id":"https://openalex.org/C49870271","wikidata":"https://www.wikidata.org/wiki/Q193657","display_name":"Convex set","level":4,"score":0.08688858151435852},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.07868942618370056},{"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/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"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/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/s10589-021-00316-0","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10589-021-00316-0","pdf_url":null,"source":{"id":"https://openalex.org/S39243548","display_name":"Computational Optimization and Applications","issn_l":"0926-6003","issn":["0926-6003","1573-2894"],"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":"Computational Optimization and Applications","raw_type":"journal-article"},{"id":"pmh:oai:RePEc:spr:coopap:v:80:y:2021:i:3:d:10.1007_s10589-021-00316-0","is_oa":false,"landing_page_url":"http://link.springer.com/10.1007/s10589-021-00316-0","pdf_url":null,"source":{"id":"https://openalex.org/S4306401271","display_name":"RePEc: Research Papers in Economics","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I77793887","host_organization_name":"Federal Reserve Bank of St. Louis","host_organization_lineage":["https://openalex.org/I77793887"],"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":"article"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/10","score":0.4399999976158142,"display_name":"Reduced inequalities"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":38,"referenced_works":["https://openalex.org/W92138443","https://openalex.org/W572922989","https://openalex.org/W1543439990","https://openalex.org/W1551360398","https://openalex.org/W1601741115","https://openalex.org/W1861508522","https://openalex.org/W1964730816","https://openalex.org/W1967073510","https://openalex.org/W1986370957","https://openalex.org/W1992688650","https://openalex.org/W1999913571","https://openalex.org/W2030451378","https://openalex.org/W2039748980","https://openalex.org/W2053643774","https://openalex.org/W2057944397","https://openalex.org/W2079340989","https://openalex.org/W2086128789","https://openalex.org/W2099799470","https://openalex.org/W2102892751","https://openalex.org/W2113734366","https://openalex.org/W2127930751","https://openalex.org/W2142124856","https://openalex.org/W2149454052","https://openalex.org/W2165281529","https://openalex.org/W2165289170","https://openalex.org/W2166161964","https://openalex.org/W2182110422","https://openalex.org/W2495457432","https://openalex.org/W2912522929","https://openalex.org/W2936995161","https://openalex.org/W2963774730","https://openalex.org/W2964208659","https://openalex.org/W3008034264","https://openalex.org/W4207043381","https://openalex.org/W4241481124","https://openalex.org/W4248269519","https://openalex.org/W4285719527","https://openalex.org/W4301791716"],"related_works":["https://openalex.org/W2124038748","https://openalex.org/W2771160919","https://openalex.org/W4301659259","https://openalex.org/W2941716933","https://openalex.org/W2953397625","https://openalex.org/W2951676025","https://openalex.org/W2189286193","https://openalex.org/W2169279714","https://openalex.org/W4390640000","https://openalex.org/W4225397084"],"abstract_inverted_index":null,"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}