{"id":"https://openalex.org/W7215976922","doi":"https://doi.org/10.48550/arxiv.2610.00172","title":"Certificate-Coupled DCA for the Trust-Region Subproblem: Early Structural Escape and Progressive Global Certification","display_name":"Certificate-Coupled DCA for the Trust-Region Subproblem: Early Structural Escape and Progressive Global Certification","publication_year":2026,"publication_date":"2026-09-16","ids":{"openalex":"https://openalex.org/W7215976922","doi":"https://doi.org/10.48550/arxiv.2610.00172"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.00172","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.00172","pdf_url":"https://arxiv.org/pdf/2610.00172","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"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":"text"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2610.00172","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5154354216","display_name":"Binh T. Nguyen","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I123565023","display_name":"Vietnam National University Ho Chi Minh City","ror":"https://ror.org/00waaqh38","country_code":"VN","type":"education","lineage":["https://openalex.org/I123565023"]},{"id":"https://openalex.org/I23582244","display_name":"Ho Chi Minh City University of Science","ror":"https://ror.org/05jfbgm49","country_code":"VN","type":"education","lineage":["https://openalex.org/I123565023","https://openalex.org/I23582244"]}],"countries":["VN"],"is_corresponding":true,"raw_author_name":"Nguyen, Binh T.","raw_affiliation_strings":["Facilty of Mathematics and Computer Science , University of Science , Vietnam National Uni- versity Ho Chi Minh City , Ho Chi Minh City , Vietnam"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Facilty of Mathematics and Computer Science , University of Science , Vietnam National Uni- versity Ho Chi Minh City , Ho Chi Minh City , Vietnam","institution_ids":["https://openalex.org/I123565023","https://openalex.org/I23582244"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5154354216"],"corresponding_institution_ids":["https://openalex.org/I123565023","https://openalex.org/I23582244"],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9854000210762024,"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":0.9854000210762024,"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/T10792","display_name":"Matrix Theory and Algorithms","score":0.004900000058114529,"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/T10545","display_name":"Optimization and Variational Analysis","score":0.00419999985024333,"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/trust-region-subproblem","display_name":"trust-region subproblem","score":0.8960000276565552},{"id":"https://openalex.org/keywords/difference-of-convex-algorithm","display_name":"difference of convex algorithm","score":0.8849999904632568},{"id":"https://openalex.org/keywords/nonconvex-optimization","display_name":"non-convex optimization","score":0.8180000185966492},{"id":"https://openalex.org/keywords/lanczos-algorithm","display_name":"Lanczos method","score":0.6299999952316284},{"id":"https://openalex.org/keywords/rayleigh-quotient","display_name":"Rayleigh quotient","score":0.7400000095367432},{"id":"https://openalex.org/keywords/eigenvalue-upper-bounds","display_name":"upper bounds on eigenvalues","score":0.652999997138977}],"concepts":[{"id":"https://openalex.org/C147060835","wikidata":"https://www.wikidata.org/wiki/Q1757151","display_name":"Krylov subspace","level":3,"score":0.6504999995231628},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6449999809265137},{"id":"https://openalex.org/C119256216","wikidata":"https://www.wikidata.org/wiki/Q913012","display_name":"Lanczos resampling","level":3,"score":0.6241999864578247},{"id":"https://openalex.org/C140479938","wikidata":"https://www.wikidata.org/wiki/Q5254619","display_name":"Iterated function","level":2,"score":0.5942999720573425},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.531499981880188},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.5232999920845032},{"id":"https://openalex.org/C32834561","wikidata":"https://www.wikidata.org/wiki/Q660730","display_name":"Subspace topology","level":2,"score":0.5200999975204468},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4528000056743622},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.43939998745918274},{"id":"https://openalex.org/C98045186","wikidata":"https://www.wikidata.org/wiki/Q205663","display_name":"Process (computing)","level":2,"score":0.38690000772476196},{"id":"https://openalex.org/C195065555","wikidata":"https://www.wikidata.org/wiki/Q214881","display_name":"Curvature","level":2,"score":0.35409998893737793},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.34700000286102295},{"id":"https://openalex.org/C2778158742","wikidata":"https://www.wikidata.org/wiki/Q1665115","display_name":"Rayleigh quotient","level":3,"score":0.34360000491142273},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.33570000529289246},{"id":"https://openalex.org/C167431342","wikidata":"https://www.wikidata.org/wiki/Q1754327","display_name":"Preconditioner","level":3,"score":0.3312000036239624},{"id":"https://openalex.org/C111030470","wikidata":"https://www.wikidata.org/wiki/Q1430460","display_name":"Curse of dimensionality","level":2,"score":0.3280999958515167},{"id":"https://openalex.org/C72134830","wikidata":"https://www.wikidata.org/wiki/Q5166524","display_name":"Convexity","level":2,"score":0.3262999951839447},{"id":"https://openalex.org/C18762648","wikidata":"https://www.wikidata.org/wiki/Q42213","display_name":"Work (physics)","level":2,"score":0.30970001220703125},{"id":"https://openalex.org/C128356825","wikidata":"https://www.wikidata.org/wiki/Q738422","display_name":"Barycentric coordinate system","level":2,"score":0.30390000343322754},{"id":"https://openalex.org/C2776436953","wikidata":"https://www.wikidata.org/wiki/Q5163215","display_name":"Consistency (knowledge bases)","level":2,"score":0.28220000863075256},{"id":"https://openalex.org/C2776135515","wikidata":"https://www.wikidata.org/wiki/Q17143721","display_name":"Regularization (linguistics)","level":2,"score":0.28130000829696655},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.26969999074935913},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.26159998774528503},{"id":"https://openalex.org/C46304622","wikidata":"https://www.wikidata.org/wiki/Q374814","display_name":"Certification","level":2,"score":0.26100000739097595},{"id":"https://openalex.org/C152442038","wikidata":"https://www.wikidata.org/wiki/Q2778212","display_name":"Tikhonov regularization","level":3,"score":0.25270000100135803}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.00172","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.00172","pdf_url":"https://arxiv.org/pdf/2610.00172","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"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":"text"},{"id":"doi:10.48550/arxiv.2610.00172","doi":"https://doi.org/10.48550/arxiv.2610.00172","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.00172","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2610.00172","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.00172","pdf_url":"https://arxiv.org/pdf/2610.00172","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"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":"text"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7215976922.pdf","grobid_xml":"https://content.openalex.org/works/W7215976922.grobid-xml"},"referenced_works_count":16,"referenced_works":["https://openalex.org/W2027882669","https://openalex.org/W2040466831","https://openalex.org/W2055029225","https://openalex.org/W2058514739","https://openalex.org/W2591505158","https://openalex.org/W2626224734","https://openalex.org/W2759377581","https://openalex.org/W2809818748","https://openalex.org/W2990364438","https://openalex.org/W3013364710","https://openalex.org/W3137421758","https://openalex.org/W3161616175","https://openalex.org/W3203963792","https://openalex.org/W4386844322","https://openalex.org/W4415954963","https://openalex.org/W7161588378"],"related_works":["https://openalex.org/W2051664786","https://openalex.org/W2055029225","https://openalex.org/W7098282621","https://openalex.org/W1992341128","https://openalex.org/W2027882669","https://openalex.org/W79914553","https://openalex.org/W2508878802","https://openalex.org/W7098770730","https://openalex.org/W4414989062","https://openalex.org/W2063690908"],"abstract_inverted_index":{"We":[0,94],"study":[1],"the":[2,31,52,81,86,102,106,129,135,139,145,150,163,167,174,179,192,196,212,216],"nonconvex":[3],"trust-region":[4],"subproblem":[5],"by":[6,166,203],"a":[7,24,36,48,58,76,96,120,125,205],"certificate-coupled":[8],"difference-of-convex":[9],"algorithm":[10],"that":[11],"incorporates":[12],"spectral":[13,177,200,213],"information":[14],"before":[15,173],"exact":[16],"first-order":[17],"stationarity":[18],"is":[19,153,183],"attained.":[20],"The":[21,70],"method":[22],"maintains":[23],"persistent":[25],"randomized":[26],"Krylov":[27,72,151,193],"subspace":[28,73,152,194],"together":[29,110],"with":[30,47,63,111],"DCA":[32],"iterates.":[33],"Near":[34],"stationarity,":[35],"sufficiently":[37],"negative":[38],"shifted":[39],"Rayleigh":[40],"quotient":[41],"yields":[42],"an":[43,66],"explicit":[44],"feasible":[45],"correction":[46,99],"quantitative":[49,121,180],"decrease":[50,181],"in":[51,142,185,215],"objective":[53,131],"value;":[54],"otherwise,":[55],"completion":[56],"of":[57,199,207],"prescribed":[59],"Lanczos":[60],"depth":[61],"provides,":[62],"high":[64],"probability,":[65],"approximate":[67],"positive-semidefiniteness":[68],"certificate.":[69,123],"same":[71],"also":[74],"provides":[75],"certified":[77,130],"upper":[78],"bound":[79,182],"on":[80],"largest":[82],"eigenvalue":[83],"for":[84],"selecting":[85],"DC":[87],"curvature":[88],"parameter":[89],"at":[90,116],"subsequent":[91],"accuracy":[92,127,158],"stages.":[93,159],"prove":[95],"uniform":[97],"negative-curvature":[98,169],"result":[100],"over":[101],"trust":[103],"region,":[104],"covering":[105],"near-orthogonal":[107,188],"hard-case":[108],"regime,":[109],"finite-termination":[112],"and":[113,119,138,157,190],"work":[114],"bounds":[115],"fixed":[117],"tolerances":[118],"objective-gap":[122],"Under":[124],"progressive":[126],"schedule,":[128],"values":[132],"converge":[133,141],"to":[134,144,210],"global":[136,146],"optimum":[137],"iterates":[140],"distance":[143],"solution":[147],"set,":[148],"while":[149],"retained":[154],"across":[155],"corrections":[156,170],"Numerical":[160],"experiments":[161],"illustrate":[162],"phenomena":[164],"established":[165],"analysis:":[168],"can":[171],"occur":[172],"corresponding":[175],"post-convergence":[176],"corrections,":[178],"satisfied":[184],"all":[186],"tested":[187],"instances,":[189],"retaining":[191],"reduces":[195],"median":[197],"number":[198],"matrix-vector":[201],"products":[202],"approximately":[204],"factor":[206],"$2.6$":[208],"relative":[209],"restarting":[211],"process":[214],"controlled":[217],"comparison.":[218]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-10-03T00:00:00"}
