{"id":"https://openalex.org/W7140172904","doi":"https://doi.org/10.48550/arxiv.2603.20859","title":"Efficient Nehari manifold optimization algorithms for computing ground state solutions of nonlinear elliptic systems","display_name":"Efficient Nehari manifold optimization algorithms for computing ground state solutions of nonlinear elliptic systems","publication_year":2026,"publication_date":"2026-03-21","ids":{"openalex":"https://openalex.org/W7140172904","doi":"https://doi.org/10.48550/arxiv.2603.20859"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2603.20859","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2603.20859","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"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":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2603.20859","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Chen, Zhaoxing","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Chen, Zhaoxing","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":null,"display_name":"Liu, Wei","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Liu, Wei","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":null,"display_name":"Xie, Ziqing","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Xie, Ziqing","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":null,"display_name":"Yi, Wenfan","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Yi, Wenfan","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"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/T11205","display_name":"Numerical methods in inverse problems","score":0.24969999492168427,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/T11205","display_name":"Numerical methods in inverse problems","score":0.24969999492168427,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.12080000340938568,"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/T11206","display_name":"Model Reduction and Neural Networks","score":0.06870000064373016,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/gradient-descent","display_name":"Gradient descent","score":0.6309000253677368},{"id":"https://openalex.org/keywords/saddle-point","display_name":"Saddle point","score":0.5164999961853027},{"id":"https://openalex.org/keywords/riemannian-manifold","display_name":"Riemannian manifold","score":0.4844000041484833},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.478300005197525},{"id":"https://openalex.org/keywords/manifold","display_name":"Manifold (fluid mechanics)","score":0.4731999933719635},{"id":"https://openalex.org/keywords/benchmark","display_name":"Benchmark (surveying)","score":0.4260999858379364},{"id":"https://openalex.org/keywords/coupling","display_name":"Coupling (piping)","score":0.4198000133037567},{"id":"https://openalex.org/keywords/method-of-steepest-descent","display_name":"Method of steepest descent","score":0.387800008058548},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.38760000467300415}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6789000034332275},{"id":"https://openalex.org/C153258448","wikidata":"https://www.wikidata.org/wiki/Q1199743","display_name":"Gradient descent","level":3,"score":0.6309000253677368},{"id":"https://openalex.org/C2681867","wikidata":"https://www.wikidata.org/wiki/Q690935","display_name":"Saddle point","level":2,"score":0.5164999961853027},{"id":"https://openalex.org/C2779593128","wikidata":"https://www.wikidata.org/wiki/Q632814","display_name":"Riemannian manifold","level":2,"score":0.4844000041484833},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.478300005197525},{"id":"https://openalex.org/C529865628","wikidata":"https://www.wikidata.org/wiki/Q1790740","display_name":"Manifold (fluid mechanics)","level":2,"score":0.4731999933719635},{"id":"https://openalex.org/C185798385","wikidata":"https://www.wikidata.org/wiki/Q1161707","display_name":"Benchmark (surveying)","level":2,"score":0.4260999858379364},{"id":"https://openalex.org/C131584629","wikidata":"https://www.wikidata.org/wiki/Q4308705","display_name":"Coupling (piping)","level":2,"score":0.4198000133037567},{"id":"https://openalex.org/C158847443","wikidata":"https://www.wikidata.org/wiki/Q1997812","display_name":"Method of steepest descent","level":2,"score":0.387800008058548},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.38760000467300415},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3797000050544739},{"id":"https://openalex.org/C40332964","wikidata":"https://www.wikidata.org/wiki/Q6987780","display_name":"Nehari manifold","level":3,"score":0.36899998784065247},{"id":"https://openalex.org/C117896860","wikidata":"https://www.wikidata.org/wiki/Q11376","display_name":"Acceleration","level":2,"score":0.3653999865055084},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.3621000051498413},{"id":"https://openalex.org/C26362088","wikidata":"https://www.wikidata.org/wiki/Q17086453","display_name":"Nonlinear conjugate gradient method","level":4,"score":0.3479999899864197},{"id":"https://openalex.org/C147764199","wikidata":"https://www.wikidata.org/wiki/Q6865248","display_name":"Minification","level":2,"score":0.3409999907016754},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.335099995136261},{"id":"https://openalex.org/C165551260","wikidata":"https://www.wikidata.org/wiki/Q4428962","display_name":"Adjoint equation","level":3,"score":0.3239000141620636},{"id":"https://openalex.org/C132459708","wikidata":"https://www.wikidata.org/wiki/Q744069","display_name":"Extrapolation","level":2,"score":0.3163999915122986},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.30570000410079956},{"id":"https://openalex.org/C115680565","wikidata":"https://www.wikidata.org/wiki/Q5977448","display_name":"Gradient method","level":2,"score":0.30489999055862427},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2849000096321106},{"id":"https://openalex.org/C48103436","wikidata":"https://www.wikidata.org/wiki/Q599031","display_name":"State (computer science)","level":2,"score":0.2784000039100647},{"id":"https://openalex.org/C179603306","wikidata":"https://www.wikidata.org/wiki/Q268493","display_name":"Elliptic curve","level":2,"score":0.27810001373291016},{"id":"https://openalex.org/C17137986","wikidata":"https://www.wikidata.org/wiki/Q215067","display_name":"Orthogonality","level":2,"score":0.27390000224113464},{"id":"https://openalex.org/C64618476","wikidata":"https://www.wikidata.org/wiki/Q164296","display_name":"Variational method","level":2,"score":0.2705000042915344},{"id":"https://openalex.org/C2777127463","wikidata":"https://www.wikidata.org/wiki/Q10862618","display_name":"Saddle","level":2,"score":0.2687999904155731},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.2671000063419342},{"id":"https://openalex.org/C612670","wikidata":"https://www.wikidata.org/wiki/Q7616373","display_name":"Stiefel manifold","level":2,"score":0.25859999656677246}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2603.20859","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2603.20859","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"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":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2603.20859","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2603.20859","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"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":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"This":[0],"paper":[1],"presents":[2],"a":[3,17,80,126,151,166,176],"class":[4],"of":[5,16,26,45,99,192,201,215],"efficient":[6,128],"manifold":[7,53,57],"optimization":[8,58],"algorithms":[9,187,208],"for":[10,87],"computing":[11],"the":[12,27,42,46,51,96,100,103,109,115,118,121,156,161,172,185,190,196,206,211],"ground":[13,212],"state":[14,213],"solutions":[15,101,214],"semilinear":[18,216],"elliptic":[19,217],"system,":[20],"which":[21],"are":[22],"unstable":[23,35],"saddle":[24,36],"points":[25,37],"variational":[28,47],"functional.":[29],"Variational":[30],"arguments":[31],"show":[32,183],"that":[33,184],"these":[34],"can":[38],"be":[39],"characterized":[40],"as":[41],"local":[43],"minimizers":[44],"functional":[48],"constrained":[49,89],"to":[50,124,140,209],"Nehari":[52,56],"$\\mathcal{N}$.":[54],"The":[55,136],"method":[59],"(NMOM)":[60],"proposed":[61],"in":[62],"[Z.":[63],"Chen,":[64],"W.":[65,70],"Liu,":[66],"Z.":[67],"Xie,":[68],"and":[69,102,120,222,225,233,240],"Yi.":[71],"SIAM":[72],"J.":[73],"Sci.":[74],"Comput.,":[75],"47(4):":[76],"A2098-A2126,":[77],"2025]":[78],"provides":[79],"Riemannian":[81,129,152,197],"gradient":[82,131],"descent":[83,199],"framework":[84],"on":[85,133,147],"$\\mathcal{N}$":[86,134],"such":[88],"minimization":[90],"problems.":[91],"To":[92,159],"deal":[93],"with":[94,178,195,219],"both":[95],"intrinsic":[97],"instability":[98],"increased":[104],"computational":[105],"complexity":[106],"introduced":[107],"by":[108,150],"coupling":[110,231],"between":[111],"components,":[112,224],"we":[113,163,204],"combine":[114],"ideas":[116],"from":[117],"NMOM":[119],"Nesterov-type":[122],"acceleration":[123],"develop":[125],"new":[127],"accelerated":[130],"algorithm":[132,200],"(RAG-$\\mathcal{N}$).":[135],"key":[137],"idea":[138],"is":[139],"perform":[141],"an":[142],"easy-to-implement":[143],"nonlinear":[144],"extrapolation":[145],"step":[146],"$\\mathcal{N}$,":[148],"followed":[149],"steepest-descent":[153],"update":[154],"at":[155],"extrapolated":[157],"point.":[158],"enhance":[160],"robustness,":[162],"further":[164],"incorporate":[165],"nonmonotone":[167],"step-size":[168],"search":[169],"strategy":[170],"into":[171],"RAG-$\\mathcal{N}$":[173,186,207],"algorithm,":[174],"obtaining":[175],"variant":[177],"improved":[179],"stability.":[180],"Numerical":[181],"experiments":[182],"substantially":[188],"reduce":[189],"number":[191],"iterations":[193],"compared":[194],"steepest":[198],"NMOM.":[202],"Finally,":[203],"apply":[205],"compute":[210],"systems":[218],"two,":[220],"three":[221],"four":[223],"investigate":[226],"their":[227],"behavior":[228],"under":[229],"different":[230],"coefficients":[232],"various":[234],"settings,":[235],"including":[236],"Gaussian-type":[237],"external":[238],"potentials":[239],"singular":[241],"diffusion":[242],"coefficients.":[243]},"counts_by_year":[],"updated_date":"2026-04-25T08:17:42.794288","created_date":"2026-03-25T00:00:00"}