{"id":"W3122767153","doi":"10.2139/ssrn.2520482","title":"A Variational Approach to Lagrange Multipliers","year":2014,"lang":"en","type":"article","venue":"SSRN Electronic Journal","topic":"Optimization and Variational Analysis","field":"Computer Science","cited_by":0,"is_retracted":false,"has_abstract":false,"ca_institutions":"Royal Society of Canada","funders":"","keywords":"Lagrange multiplier; Constraint algorithm; Applied mathematics; Mathematics; Mathematical economics; Mathematical optimization; Calculus (dental); Computer science; Medicine","routes":{"ca_aff":true,"ca_fund":false,"ca_venue":false,"about_ca":false,"invisible_to_affiliation_only":false},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"codex-gemma-dda1882f352a","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.00154337,0.0001027291,0.000119798,0.0002120556,0.0002464149,0.0001720569,0.000622282,0.00004187879,0.0000113831],"category_scores_gemma":[0.0001086643,0.00008911394,0.00009670491,0.0005884672,0.000008362392,0.0002529567,0.00006383908,0.0004613895,0.00008448354],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0003063905,"about_ca_system_score_gemma":0.0005827073,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00001926914,"about_ca_topic_score_gemma":0.00003865158,"domain_scores_codex":[0.9981545,0.0001046162,0.0002065874,0.0002345019,0.0003771007,0.000922736],"domain_scores_gemma":[0.9993662,0.00005244393,0.00009833597,0.0001902566,0.0001580803,0.0001347215],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"simulation_or_modeling","study_design_scores_codex":[0.000003900623,0.00005978624,0.0001796958,7.279349e-7,0.00005972618,7.094702e-8,0.0001712793,0.03147577,0.00001730827,0.959409,0.00009036237,0.008532379],"study_design_scores_gemma":[0.0005257925,0.00008453522,0.001665429,0.000002251561,0.00001772036,0.00007766778,0.00008083084,0.7928792,0.000005299346,0.1993183,0.005155512,0.0001874379],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":null,"genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.0002642421,0.00003956333,0.9903029,0.003131096,0.0001050568,0.00005875105,5.590873e-7,0.0000492151,0.006048602],"genre_scores_gemma":[0.8239648,0.00006563135,0.1719713,0.001587644,0.0003768762,0.00001115446,0.000008324306,0.00001146595,0.002002806],"genre_candidate":"methods","genre_consensus":null,"teacher_disagreement_score":0.8237005,"threshold_uncertainty_score":0.3633961,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.006466003260341021,"score_gpt":0.2077591992675414,"score_spread":0.2012931960072004,"validation_status":"score_only:v0-immature-baseline","note":"Baseline scores from an immature model (maturity gate not passed). Scores rank; they never assert a category."}}