{"id":"https://openalex.org/W7203440406","doi":"https://doi.org/10.48550/arxiv.2608.12520","title":"Weight Certificates for Convex Multi-Objective MPC: Geometric Characterization, $\\ell^1$ Construction, and $\\ell^2$ Foreclosure","display_name":"Weight Certificates for Convex Multi-Objective MPC: Geometric Characterization, $\\ell^1$ Construction, and $\\ell^2$ Foreclosure","publication_year":2026,"publication_date":"2026-08-12","ids":{"openalex":"https://openalex.org/W7203440406","doi":"https://doi.org/10.48550/arxiv.2608.12520"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2608.12520","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.12520","pdf_url":"https://arxiv.org/pdf/2608.12520","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","license_id":"https://openalex.org/licenses/cc-by","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/2608.12520","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5015115695","display_name":"Hadi Hajieghrary","orcid":"https://orcid.org/0000-0002-4278-1293","observed_orcids":["https://orcid.org/0000-0002-4278-1293"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Hajieghrary, Hadi","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5140619918","display_name":"Benedikt Walter","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Walter, Benedikt","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5111261078","display_name":"Chaitanya Shinde","orcid":"https://orcid.org/0009-0003-8176-524X","observed_orcids":["https://orcid.org/0009-0003-8176-524X"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Shinde, Chaitanya","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5147218264","display_name":"Miguel Hurtadoand Jerry Lopez","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Lopez, Miguel Hurtadoand Jerry","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"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/T10791","display_name":"Advanced Control Systems Optimization","score":0.9286999702453613,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10791","display_name":"Advanced Control Systems Optimization","score":0.9286999702453613,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.011699999682605267,"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":0.008700000122189522,"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/multi-objective-model-predictive-control","display_name":"multi-objective model predictive control","score":0.8600000143051147},{"id":"https://openalex.org/keywords/convex-optimization","display_name":"convex optimization","score":0.6620000004768372},{"id":"https://openalex.org/keywords/lexicographic-optimization","display_name":"lexicographic optimization","score":0.7609999775886536},{"id":"https://openalex.org/keywords/normal-cone","display_name":"normal cone","score":0.843999981880188},{"id":"https://openalex.org/keywords/karush-kuhn-tucker-conditions","display_name":"Karush-Kuhn-Tucker conditions","score":0.6940000057220459}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7842000126838684},{"id":"https://openalex.org/C173801870","wikidata":"https://www.wikidata.org/wiki/Q201413","display_name":"Heuristic","level":2,"score":0.5088000297546387},{"id":"https://openalex.org/C136625980","wikidata":"https://www.wikidata.org/wiki/Q663208","display_name":"Rounding","level":2,"score":0.47350001335144043},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4681999981403351},{"id":"https://openalex.org/C159254197","wikidata":"https://www.wikidata.org/wiki/Q1144915","display_name":"Lexicographical order","level":2,"score":0.4453999996185303},{"id":"https://openalex.org/C111110010","wikidata":"https://www.wikidata.org/wiki/Q2627315","display_name":"Convex combination","level":4,"score":0.38350000977516174},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.37860000133514404},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.36419999599456787},{"id":"https://openalex.org/C110943637","wikidata":"https://www.wikidata.org/wiki/Q4129097","display_name":"Convex polytope","level":5,"score":0.35510000586509705},{"id":"https://openalex.org/C124584101","wikidata":"https://www.wikidata.org/wiki/Q1053266","display_name":"Multiplier (economics)","level":2,"score":0.3528999984264374},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.334199994802475},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3321000039577484},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.3319000005722046},{"id":"https://openalex.org/C140779682","wikidata":"https://www.wikidata.org/wiki/Q210868","display_name":"Sampling (signal processing)","level":3,"score":0.328000009059906},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.3179999887943268},{"id":"https://openalex.org/C189430467","wikidata":"https://www.wikidata.org/wiki/Q7293293","display_name":"Ranking (information retrieval)","level":2,"score":0.31380000710487366},{"id":"https://openalex.org/C2778067643","wikidata":"https://www.wikidata.org/wiki/Q166507","display_name":"Interval (graph theory)","level":2,"score":0.3052000105381012},{"id":"https://openalex.org/C34146451","wikidata":"https://www.wikidata.org/wiki/Q5048094","display_name":"Cascade","level":2,"score":0.3041999936103821},{"id":"https://openalex.org/C57493831","wikidata":"https://www.wikidata.org/wiki/Q3134666","display_name":"Projection (relational algebra)","level":2,"score":0.3037000000476837},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.2948000133037567},{"id":"https://openalex.org/C2776330181","wikidata":"https://www.wikidata.org/wiki/Q18358244","display_name":"Maximization","level":2,"score":0.29339998960494995},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.2768999934196472},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.2768999934196472},{"id":"https://openalex.org/C183115368","wikidata":"https://www.wikidata.org/wiki/Q856577","display_name":"Weighting","level":2,"score":0.2653000056743622},{"id":"https://openalex.org/C106131492","wikidata":"https://www.wikidata.org/wiki/Q3072260","display_name":"Filter (signal processing)","level":2,"score":0.2646999955177307},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.2565999925136566},{"id":"https://openalex.org/C22679943","wikidata":"https://www.wikidata.org/wiki/Q159375","display_name":"Standard deviation","level":2,"score":0.25110000371932983}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2608.12520","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.12520","pdf_url":"https://arxiv.org/pdf/2608.12520","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","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2608.12520","doi":"https://doi.org/10.48550/arxiv.2608.12520","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2608.12520","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","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2608.12520","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.12520","pdf_url":"https://arxiv.org/pdf/2608.12520","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","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7203440406.pdf","grobid_xml":"https://content.openalex.org/works/W7203440406.grobid-xml"},"referenced_works_count":2,"referenced_works":["https://openalex.org/W4281801799","https://openalex.org/W7208707055"],"related_works":["https://openalex.org/W2033293024","https://openalex.org/W2144884795","https://openalex.org/W7168243446","https://openalex.org/W4285102215","https://openalex.org/W7172314352","https://openalex.org/W1972016858","https://openalex.org/W2523170268","https://openalex.org/W2571349240","https://openalex.org/W1997861095","https://openalex.org/W4206530512"],"abstract_inverted_index":{"Automated-driving":[0],"rulebooks":[1],"rank":[2],"rule":[3],"violations":[4],"lexicographically,":[5],"and":[6,103,157,207],"model":[7],"predictive":[8],"control":[9],"enforces":[10],"that":[11],"ranking":[12],"either":[13],"exactly,":[14],"through":[15,23],"$L{+}1$":[16],"sequential":[17],"programs":[18],"per":[19],"tick,":[20],"or":[21],"approximately,":[22],"a":[24,44,48,61,95,100,104,112,164,173,228],"weighted":[25,49,216],"sum":[26,50],"tuned":[27],"by":[28,60,98],"the":[29,37,40,52,66,70,74,77,81,124,132,143,187,193,204,223],"separation":[30],"heuristic":[31,38,166],"$w_1\\gg":[32],"w_2\\gg\\cdots\\gg":[33],"w_L$.":[34],"We":[35],"show":[36],"answers":[39],"wrong":[41],"question.":[42],"For":[43],"convex":[45],"priority-ordered":[46],"program,":[47],"reproduces":[51],"lexicographic":[53,75],"optimum":[54],"precisely":[55],"when":[56],"its":[57],"weight,":[58],"augmented":[59],"unit":[62],"performance":[63],"coefficient,":[64],"supports":[65],"upper":[67],"image":[68],"of":[69,84,152,190,230],"achievement":[71],"map":[72],"at":[73,203],"point;":[76],"admissible":[78],"weights":[79,145],"form":[80],"unit-performance":[82],"slice":[83,93],"an":[85,108,191],"outward":[86],"normal":[87],"cone.":[88],"Under":[89],"hinge":[90],"penalties":[91,117],"this":[92],"is":[94,121,127,184,196],"polyhedron":[96],"obtained":[97],"projecting":[99],"scaled-KKT":[101],"system,":[102],"linear":[105],"program":[106],"returns":[107],"interior":[109],"weight":[110,120,167,183],"with":[111,129,218],"certified":[113],"margin;":[114],"under":[115],"squared-hinge":[116],"no":[118,181],"finite":[119],"exact":[122],"whenever":[123],"limiting":[125],"multiplier":[126],"nonzero,":[128],"violation":[130],"along":[131],"local":[133],"minimizer":[134],"branch":[135],"decaying":[136],"as":[137],"$O(1/w)$.":[138],"Calibrated":[139],"on":[140,172],"held-out":[141],"logs,":[142],"resulting":[144],"have":[146],"near-equal":[147],"tier":[148],"components":[149],"in":[150,168],"nine":[151],"eleven":[153],"calibration-eligible":[154],"scenario":[155],"classes":[156],"roughly":[158],"double":[159],"legal-tier":[160],"event":[161],"precision":[162],"against":[163],"matched":[165],"closed-loop":[169],"nuPlan":[170],"experiments":[171],"25-rule":[174],"rulebook.":[175],"The":[176],"certificate":[177],"is,":[178],"however,":[179],"pointwise:":[180],"single":[182],"valid":[185],"across":[186],"sampled":[188],"ticks":[189,202],"episode,":[192],"median":[194],"lifetime":[195],"one":[197],"sampling":[198],"interval":[199],"(zero":[200],"subsequent":[201],"native":[205],"rate),":[206],"persistence":[208],"tracks":[209],"active-set":[210],"stability.":[211],"These":[212],"findings":[213],"motivate":[214],"monitored":[215],"solves":[217],"selective":[219],"cascade":[220],"fallback,":[221],"although":[222],"compliance-pattern":[224],"monitor":[225],"detects":[226],"only":[227],"subset":[229],"measured":[231],"lapses.":[232]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-08-15T00:00:00"}
