{"id":"https://openalex.org/W7223148273","doi":"https://doi.org/10.48550/arxiv.2610.27727","title":"Forest Characterization of When SDP-RLT Strengthens RLT for Bilinear Terms","display_name":"Forest Characterization of When SDP-RLT Strengthens RLT for Bilinear Terms","publication_year":2026,"publication_date":"2026-10-20","ids":{"openalex":"https://openalex.org/W7223148273","doi":"https://doi.org/10.48550/arxiv.2610.27727"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.27727","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.27727","pdf_url":"https://arxiv.org/pdf/2610.27727","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/2610.27727","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5056335154","display_name":"Hayato Watanabe","orcid":"https://orcid.org/0009-0000-7421-1319","observed_orcids":["https://orcid.org/0009-0000-7421-1319"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Watanabe, Hayato","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5159164921","display_name":"Takami Sato","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I203951103","display_name":"Keio University","ror":"https://ror.org/02kn6nx58","country_code":"JP","type":"education","lineage":["https://openalex.org/I203951103"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Sato, Takami","raw_affiliation_strings":["Department of Electronics and Electrical Engineering , Keio University , 3-14-1 Hiyoshi , Kohoku-ku , Yokohama , 223-8522 , Kanagawa , Japan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electronics and Electrical Engineering , Keio University , 3-14-1 Hiyoshi , Kohoku-ku , Yokohama , 223-8522 , Kanagawa , Japan","institution_ids":["https://openalex.org/I203951103"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5159197617","display_name":"Kazuhide Nakata","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Nakata, Kazuhide","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5159165851","display_name":"Ken Kobayashi","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I4400009020","display_name":"Institute of Science Tokyo","ror":"https://ror.org/05dqf9946","country_code":"JP","type":"education","lineage":["https://openalex.org/I4400009020"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Kobayashi, Ken","raw_affiliation_strings":["Department of Industrial Engineering and Economics , Institute of Science Tokyo , 2-12-1 Ookayama , Meguro-ku , 152-8550 , Tokyo , Japan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Industrial Engineering and Economics , Institute of Science Tokyo , 2-12-1 Ookayama , Meguro-ku , 152-8550 , Tokyo , Japan","institution_ids":["https://openalex.org/I4400009020"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"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":1.0,"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":1.0,"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":0.0,"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/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.0,"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/reformulation-linearization-technique","display_name":"reformulation-linearization technique","score":0.8960000276565552},{"id":"https://openalex.org/keywords/bilinear-terms","display_name":"bilinear terms","score":0.9300000071525574},{"id":"https://openalex.org/keywords/semidefinite-programming","display_name":"semidefinite programming","score":0.8679999709129333},{"id":"https://openalex.org/keywords/complete-bipartite-subgraphs","display_name":"complete bipartite subgraphs","score":0.9520000219345093},{"id":"https://openalex.org/keywords/hadamard-matrices","display_name":"Hadamard matrices","score":0.8370000123977661},{"id":"https://openalex.org/keywords/relaxation-strength","display_name":"relaxation strength","score":0.5640000104904175},{"id":"https://openalex.org/keywords/nonconvex-optimization","display_name":"non-convex optimization","score":0.5460000038146973}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8427000045776367},{"id":"https://openalex.org/C205203396","wikidata":"https://www.wikidata.org/wiki/Q612143","display_name":"Bilinear interpolation","level":2,"score":0.7056000232696533},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5008000135421753},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.47859999537467957},{"id":"https://openalex.org/C197657726","wikidata":"https://www.wikidata.org/wiki/Q174733","display_name":"Bipartite graph","level":3,"score":0.46470001339912415},{"id":"https://openalex.org/C101901036","wikidata":"https://www.wikidata.org/wiki/Q2269096","display_name":"Semidefinite programming","level":2,"score":0.46369999647140503},{"id":"https://openalex.org/C8828549","wikidata":"https://www.wikidata.org/wiki/Q837924","display_name":"Bilinear form","level":2,"score":0.4553000032901764},{"id":"https://openalex.org/C130367717","wikidata":"https://www.wikidata.org/wiki/Q189791","display_name":"Diagonal","level":2,"score":0.4537000060081482},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.44830000400543213},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.4440999925136566},{"id":"https://openalex.org/C2776029896","wikidata":"https://www.wikidata.org/wiki/Q3935810","display_name":"Relaxation (psychology)","level":2,"score":0.4291999936103821},{"id":"https://openalex.org/C134119311","wikidata":"https://www.wikidata.org/wiki/Q913598","display_name":"Complete bipartite graph","level":4,"score":0.4226999878883362},{"id":"https://openalex.org/C49712288","wikidata":"https://www.wikidata.org/wiki/Q77601250","display_name":"Positive-definite matrix","level":3,"score":0.4124999940395355},{"id":"https://openalex.org/C77246614","wikidata":"https://www.wikidata.org/wiki/Q1409400","display_name":"Gramian matrix","level":3,"score":0.3822000026702881},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3522000014781952},{"id":"https://openalex.org/C2780841128","wikidata":"https://www.wikidata.org/wiki/Q5073781","display_name":"Characterization (materials science)","level":2,"score":0.3391000032424927},{"id":"https://openalex.org/C180356752","wikidata":"https://www.wikidata.org/wiki/Q727035","display_name":"Adjacency matrix","level":3,"score":0.31769999861717224},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.30970001220703125},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3012000024318695},{"id":"https://openalex.org/C182365436","wikidata":"https://www.wikidata.org/wiki/Q50701","display_name":"Variable (mathematics)","level":2,"score":0.3005000054836273},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.2849999964237213},{"id":"https://openalex.org/C113313756","wikidata":"https://www.wikidata.org/wiki/Q332791","display_name":"Diagonal matrix","level":3,"score":0.2818000018596649},{"id":"https://openalex.org/C84392682","wikidata":"https://www.wikidata.org/wiki/Q1952404","display_name":"Multilinear map","level":2,"score":0.27889999747276306},{"id":"https://openalex.org/C2780009758","wikidata":"https://www.wikidata.org/wiki/Q6804172","display_name":"Measure (data warehouse)","level":2,"score":0.27869999408721924},{"id":"https://openalex.org/C72134830","wikidata":"https://www.wikidata.org/wiki/Q5166524","display_name":"Convexity","level":2,"score":0.2621000111103058},{"id":"https://openalex.org/C125080357","wikidata":"https://www.wikidata.org/wiki/Q45715","display_name":"Complete graph","level":3,"score":0.2621000111103058}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.27727","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.27727","pdf_url":"https://arxiv.org/pdf/2610.27727","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.2610.27727","doi":"https://doi.org/10.48550/arxiv.2610.27727","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.27727","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":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2610.27727","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.27727","pdf_url":"https://arxiv.org/pdf/2610.27727","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/W7223148273.pdf","grobid_xml":"https://content.openalex.org/works/W7223148273.grobid-xml"},"referenced_works_count":15,"referenced_works":["https://openalex.org/W1966182797","https://openalex.org/W1978797771","https://openalex.org/W1988622494","https://openalex.org/W2006704773","https://openalex.org/W2071143636","https://openalex.org/W2078992232","https://openalex.org/W2105880662","https://openalex.org/W2166798101","https://openalex.org/W2787178663","https://openalex.org/W2964069177","https://openalex.org/W4220970815","https://openalex.org/W4313323051","https://openalex.org/W4390701894","https://openalex.org/W4399179446","https://openalex.org/W4403995591"],"related_works":["https://openalex.org/W1879219441","https://openalex.org/W7204947624","https://openalex.org/W7171715091","https://openalex.org/W7125856386","https://openalex.org/W4399179446","https://openalex.org/W6945415412","https://openalex.org/W2336326768","https://openalex.org/W2097687466","https://openalex.org/W4400685278","https://openalex.org/W4377200007"],"abstract_inverted_index":{"We":[0,26,130],"study":[1],"two":[2,83,118],"relaxations":[3,84,119],"for":[4,40,46,53],"bilinear":[5,31,48,148],"terms":[6,32],"in":[7],"box-constrained":[8],"variables:":[9],"the":[10,16,28,54,61,65,69,77,82,96,113,117,125,135,140,162],"reformulation-linearization":[11],"technique":[12],"(RLT)":[13],"relaxation":[14,56],"and":[15,43,81,122],"SDP-RLT":[17,66],"relaxation,":[18,67],"which":[19],"combines":[20],"RLT":[21,55,79],"with":[22,37,161],"semidefinite":[23,106],"programming":[24],"(SDP).":[25],"represent":[27],"pattern":[29],"of":[30,60,64,116,164],"by":[33,151],"an":[34],"undirected":[35],"graph,":[36],"one":[38,44],"vertex":[39],"each":[41,47],"variable":[42],"edge":[45],"term.":[49],"A":[50],"point":[51],"feasible":[52,114],"fixes":[57],"only":[58,123],"part":[59],"lifted":[62],"matrix":[63,97,107,154],"leaving":[68],"remaining":[70],"entries":[71,89],"to":[72,76],"be":[73,92,138],"chosen":[74,93],"subject":[75],"diagonal":[78],"inequalities,":[80],"differ":[85],"exactly":[86],"when":[87,139],"these":[88],"cannot":[90],"always":[91],"so":[94],"that":[95,112,165],"becomes":[98],"positive":[99,105],"semidefinite.":[100],"Formulating":[101],"this":[102],"as":[103],"a":[104,128,143,147,152],"completion":[108],"problem,":[109],"we":[110],"show":[111],"regions":[115],"coincide":[120],"if":[121,124],"graph":[126,141],"is":[127],"forest.":[129],"also":[131],"measure":[132],"how":[133],"large":[134],"difference":[136],"can":[137],"contains":[142],"complete":[144],"bipartite":[145],"subgraph:":[146],"objective":[149],"given":[150],"Hadamard":[153],"yields":[155],"optimal":[156],"values":[157],"whose":[158],"ratio":[159],"grows":[160],"size":[163],"subgraph.":[166]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-10-22T00:00:00"}