{"id":"https://openalex.org/W2065670060","doi":"https://doi.org/10.1090/s0025-5718-2014-02848-2","title":"A perturbation approach for an inverse quadratic programming problem over second-order cones","display_name":"A perturbation approach for an inverse quadratic programming problem over second-order cones","publication_year":2014,"publication_date":"2014-07-18","ids":{"openalex":"https://openalex.org/W2065670060","doi":"https://doi.org/10.1090/s0025-5718-2014-02848-2","mag":"2065670060"},"language":"en","primary_location":{"id":"doi:10.1090/s0025-5718-2014-02848-2","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-2014-02848-2","pdf_url":"https://www.ams.org/mcom/2015-84-291/S0025-5718-2014-02848-2/S0025-5718-2014-02848-2.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://www.ams.org/mcom/2015-84-291/S0025-5718-2014-02848-2/S0025-5718-2014-02848-2.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5101677631","display_name":"Yi Zhang","orcid":"https://orcid.org/0000-0002-6541-2378"},"institutions":[{"id":"https://openalex.org/I143593769","display_name":"East China University of Science and Technology","ror":"https://ror.org/01vyrm377","country_code":"CN","type":"education","lineage":["https://openalex.org/I143593769"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yi Zhang","raw_affiliation_strings":["Department of Mathematics, School of Science, East China University of Science and Technology, Shanghai, 200237, China","Department of Mathematics, School of Science, East China University of Science and Technology, Shanghai 200237, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, School of Science, East China University of Science and Technology, Shanghai, 200237, China","institution_ids":["https://openalex.org/I143593769"]},{"raw_affiliation_string":"Department of Mathematics, School of Science, East China University of Science and Technology, Shanghai 200237, China","institution_ids":["https://openalex.org/I143593769"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100370811","display_name":"Liwei Zhang","orcid":"https://orcid.org/0000-0002-9207-5290"},"institutions":[{"id":"https://openalex.org/I27357992","display_name":"Dalian University of Technology","ror":"https://ror.org/023hj5876","country_code":"CN","type":"education","lineage":["https://openalex.org/I27357992"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Liwei Zhang","raw_affiliation_strings":["School of Mathematical Sciences, Dalian University of Technology, Dalian 116024, China","School of Mathematical Sciences, Dalian University of Technology , Dalian , 116024 , China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences, Dalian University of Technology, Dalian 116024, China","institution_ids":["https://openalex.org/I27357992"]},{"raw_affiliation_string":"School of Mathematical Sciences, Dalian University of Technology , Dalian , 116024 , China","institution_ids":["https://openalex.org/I27357992"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5005895773","display_name":"Jia Wu","orcid":"https://orcid.org/0000-0002-1310-3709"},"institutions":[{"id":"https://openalex.org/I27357992","display_name":"Dalian University of Technology","ror":"https://ror.org/023hj5876","country_code":"CN","type":"education","lineage":["https://openalex.org/I27357992"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jia Wu","raw_affiliation_strings":["School of Mathematical Sciences, Dalian University of Technology, Dalian 116024, China","School of Mathematical Sciences, Dalian University of Technology , Dalian , 116024 , China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences, Dalian University of Technology, Dalian 116024, China","institution_ids":["https://openalex.org/I27357992"]},{"raw_affiliation_string":"School of Mathematical Sciences, Dalian University of Technology , Dalian , 116024 , China","institution_ids":["https://openalex.org/I27357992"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100442199","display_name":"Jianzhong Zhang","orcid":"https://orcid.org/0000-0001-7056-8206"},"institutions":[{"id":"https://openalex.org/I12615008","display_name":"Beijing Normal-Hong Kong Baptist University","ror":"https://ror.org/04snvc712","country_code":"CN","type":"education","lineage":["https://openalex.org/I12615008"]},{"id":"https://openalex.org/I141568987","display_name":"Hong Kong Baptist University","ror":"https://ror.org/0145fw131","country_code":"HK","type":"education","lineage":["https://openalex.org/I141568987"]},{"id":"https://openalex.org/I25254941","display_name":"Beijing Normal University","ror":"https://ror.org/022k4wk35","country_code":"CN","type":"education","lineage":["https://openalex.org/I25254941"]}],"countries":["CN","HK"],"is_corresponding":false,"raw_author_name":"Jianzhong Zhang","raw_affiliation_strings":["Division of Science and Technology, Beijing Normal University-Hong Kong Baptist University United International College, Zhuhai, 519085, China","Division of Science and Technology  Beijing Normal University-Hong Kong Baptist University  United International College  Zhuhai 519085  China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Division of Science and Technology, Beijing Normal University-Hong Kong Baptist University United International College, Zhuhai, 519085, China","institution_ids":["https://openalex.org/I12615008","https://openalex.org/I141568987","https://openalex.org/I25254941"]},{"raw_affiliation_string":"Division of Science and Technology  Beijing Normal University-Hong Kong Baptist University  United International College  Zhuhai 519085  China","institution_ids":["https://openalex.org/I141568987"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":5,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.462,"has_fulltext":true,"cited_by_count":5,"citation_normalized_percentile":{"value":0.63705826,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"84","issue":"291","first_page":"209","last_page":"236"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9998999834060669,"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":0.9998999834060669,"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/T10545","display_name":"Optimization and Variational Analysis","score":0.9987000226974487,"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/T10792","display_name":"Matrix Theory and Algorithms","score":0.9916999936103821,"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/mathematics","display_name":"Mathematics","score":0.8288357257843018},{"id":"https://openalex.org/keywords/second-order-cone-programming","display_name":"Second-order cone programming","score":0.5955657958984375},{"id":"https://openalex.org/keywords/smoothing","display_name":"Smoothing","score":0.582211971282959},{"id":"https://openalex.org/keywords/quadratic-programming","display_name":"Quadratic programming","score":0.5697112083435059},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.543443500995636},{"id":"https://openalex.org/keywords/rate-of-convergence","display_name":"Rate of convergence","score":0.45983001589775085},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.43239128589630127},{"id":"https://openalex.org/keywords/quadratic-equation","display_name":"Quadratic equation","score":0.4119222164154053},{"id":"https://openalex.org/keywords/convex-optimization","display_name":"Convex optimization","score":0.16073834896087646},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.08918854594230652},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.06989225745201111}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8288357257843018},{"id":"https://openalex.org/C111397411","wikidata":"https://www.wikidata.org/wiki/Q7442977","display_name":"Second-order cone programming","level":4,"score":0.5955657958984375},{"id":"https://openalex.org/C3770464","wikidata":"https://www.wikidata.org/wiki/Q775963","display_name":"Smoothing","level":2,"score":0.582211971282959},{"id":"https://openalex.org/C81845259","wikidata":"https://www.wikidata.org/wiki/Q290117","display_name":"Quadratic programming","level":2,"score":0.5697112083435059},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.543443500995636},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.45983001589775085},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.43239128589630127},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.4119222164154053},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.16073834896087646},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.08918854594230652},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.06989225745201111},{"id":"https://openalex.org/C127162648","wikidata":"https://www.wikidata.org/wiki/Q16858953","display_name":"Channel (broadcasting)","level":2,"score":0.0},{"id":"https://openalex.org/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","level":1,"score":0.0},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1090/s0025-5718-2014-02848-2","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-2014-02848-2","pdf_url":"https://www.ams.org/mcom/2015-84-291/S0025-5718-2014-02848-2/S0025-5718-2014-02848-2.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1090/s0025-5718-2014-02848-2","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-2014-02848-2","pdf_url":"https://www.ams.org/mcom/2015-84-291/S0025-5718-2014-02848-2/S0025-5718-2014-02848-2.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G5339140240","display_name":null,"funder_award_id":"91330206","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G6556206610","display_name":null,"funder_award_id":"11071029","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320321543","display_name":"China Postdoctoral Science Foundation","ror":"https://ror.org/0426zh255"},{"id":"https://openalex.org/F4320335787","display_name":"Fundamental Research Funds for the Central Universities","ror":null}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2065670060.pdf","grobid_xml":"https://content.openalex.org/works/W2065670060.grobid-xml"},"referenced_works_count":38,"referenced_works":["https://openalex.org/W217831350","https://openalex.org/W1507183619","https://openalex.org/W1543439990","https://openalex.org/W1551360398","https://openalex.org/W1560867458","https://openalex.org/W1966095601","https://openalex.org/W1966229055","https://openalex.org/W1973154999","https://openalex.org/W1973198704","https://openalex.org/W1973281249","https://openalex.org/W1982636073","https://openalex.org/W1992688650","https://openalex.org/W1997953403","https://openalex.org/W1999131235","https://openalex.org/W2003486810","https://openalex.org/W2004209776","https://openalex.org/W2009923109","https://openalex.org/W2011687789","https://openalex.org/W2012701878","https://openalex.org/W2015113450","https://openalex.org/W2023949930","https://openalex.org/W2030344026","https://openalex.org/W2042838878","https://openalex.org/W2047329156","https://openalex.org/W2056424572","https://openalex.org/W2065066829","https://openalex.org/W2090770774","https://openalex.org/W2102054728","https://openalex.org/W2128115040","https://openalex.org/W2158604542","https://openalex.org/W2166758048","https://openalex.org/W2184753658","https://openalex.org/W2911796152","https://openalex.org/W4231147659","https://openalex.org/W4246495354","https://openalex.org/W4249513058","https://openalex.org/W4254220436","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W3206492465","https://openalex.org/W2099480561","https://openalex.org/W1909324310","https://openalex.org/W2379251597","https://openalex.org/W3036464408","https://openalex.org/W1984255470","https://openalex.org/W2020990755","https://openalex.org/W1985181089","https://openalex.org/W2348400506","https://openalex.org/W3020857762"],"abstract_inverted_index":{"This":[0,52],"paper":[1],"is":[2,107,145],"devoted":[3],"to":[4,37,128,139,147,169,178],"studying":[5],"a":[6,29,46,59,68,82,91],"type":[7],"of":[8,28,112],"inverse":[9,53,181],"second-order":[10,31,63,84,117,182],"cone":[11,32,64,71,85,183],"quadratic":[12,33,158,184],"programming":[13,34,185],"problems,":[14],"in":[15,19],"which":[16,96],"the":[17,21,25,74,101,110,113,136,149,164,171,174,180],"parameters":[18],"both":[20],"objective":[22,94],"function":[23],"and":[24,67,122,131,152,156],"constraint":[26],"set":[27,121,125],"given":[30],"problem":[35,54,61,80,89,106,151],"need":[36],"be":[38,56,129],"adjusted":[39],"as":[40,42,58,81,135],"little":[41],"possible":[43],"so":[44],"that":[45],"known":[47],"feasible":[48,120],"solution":[49,124],"becomes":[50],"optimal.":[51],"can":[55],"written":[57],"minimization":[60],"with":[62,90,109],"complementarity":[65,86],"constraints":[66],"positive":[69],"semidefinite":[70],"constraint.":[72],"Applying":[73],"duality":[75],"theory,":[76],"we":[77],"reformulate":[78],"this":[79],"linear":[83],"constrained":[87],"optimization":[88],"semismoothly":[92],"differentiable":[93],"function,":[95],"has":[97],"fewer":[98],"variables":[99],"than":[100],"original":[102],"one.":[103],"A":[104,141],"perturbed":[105,150],"proposed":[108],"help":[111],"projection":[114],"operator":[115],"over":[116],"cones,":[118],"whose":[119],"optimal":[123],"are":[126,161,167],"demonstrated":[127],"continuous":[130],"outer":[132],"semicontinuous,":[133],"respectively,":[134],"parameter":[137],"decreases":[138],"zero.":[140],"smoothing":[142,175],"Newton":[143,176],"method":[144,177],"constructed":[146],"solve":[148,179],"its":[153],"global":[154],"convergence":[155,159],"local":[157],"rate":[160],"shown.":[162],"Finally,":[163],"numerical":[165],"results":[166],"reported":[168],"show":[170],"effectiveness":[172],"for":[173],"problem.":[186]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2016,"cited_by_count":1}],"updated_date":"2026-07-22T07:51:19.307946","created_date":"2025-10-10T00:00:00"}
