{"id":"W4362736486","doi":"10.1007/s10898-023-01281-0","title":"General convex relaxations of implicit functions and inverse functions","year":2023,"lang":"en","type":"article","venue":"Journal of Global Optimization","topic":"Advanced Optimization Algorithms Research","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":false,"ca_institutions":"McMaster University","funders":"Natural Sciences and Engineering Research Council of Canada; Canadian Network for Research and Innovation in Machining Technology, Natural Sciences and Engineering Research Council of Canada; McMaster University","keywords":"Mathematics; Relaxation (psychology); Monotonic function; Convex function; Convex analysis; Implicit function theorem; Applied mathematics; Uniqueness; Subderivative; Proper convex function; Mathematical optimization; Regular polygon; Convex optimization; Mathematical analysis","routes":{"ca_aff":true,"ca_fund":true,"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":[0.000410579,0.0001201794,0.0002747291,0.0002596138,0.0001614466,0.00003402915,0.0001158699,0.00009901106,0.0001684451],"category_scores_gemma":[0.001238792,0.0001127138,0.0000977102,0.00148799,0.0001012081,0.0004543128,0.00006745374,0.0001638266,0.00001463603],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.000165065,"about_ca_system_score_gemma":0.000149294,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000007925046,"about_ca_topic_score_gemma":0.00001147518,"domain_scores_codex":[0.9984884,0.00009042025,0.0006714455,0.0001338292,0.0004253291,0.0001905568],"domain_scores_gemma":[0.9978258,0.0001954673,0.000615555,0.0001755626,0.001042383,0.0001452151],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"simulation_or_modeling","study_design_gemma":"simulation_or_modeling","study_design_scores_codex":[0.00004913639,0.00008643154,0.002228957,0.000029534,0.00009138649,0.000005920744,0.00008087882,0.9736815,0.0001200863,0.00757886,0.01508013,0.0009671433],"study_design_scores_gemma":[0.001866629,0.0003307748,0.003328773,0.000063123,0.0001775419,0.0001964227,0.001103482,0.9780465,0.00005610787,0.01341059,0.001203644,0.0002163633],"study_design_candidate":"simulation_or_modeling","study_design_consensus":"simulation_or_modeling","genre_codex":"methods","genre_gemma":"methods","genre_scores_codex":[0.02823629,0.0000509434,0.9681309,0.0008658858,0.0003660051,0.0002175707,0.00008635476,0.0000668284,0.00197926],"genre_scores_gemma":[0.1025173,0.000943251,0.8892494,0.0001291037,0.0004715014,0.00002460732,0.0001174836,0.00007793936,0.006469364],"genre_candidate":"methods","genre_consensus":"methods","teacher_disagreement_score":0.07888141,"threshold_uncertainty_score":0.4596336,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.03839066513758016,"score_gpt":0.347258696766238,"score_spread":0.3088680316286578,"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."}}