{"id":"W4412767601","doi":"10.23952/jano.7.2025.2.04","title":"Calculus rules of generalized proper $\\epsilon$-subdifferential for vector valued mappings and applications","year":2025,"lang":"en","type":"article","venue":"Journal of Applied and Numerical Optimization","topic":"Optimization and Variational Analysis","field":"Computer Science","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"","keywords":"Subderivative; Calculus (dental); Mathematics; Pure mathematics; Geometry; Medicine; Regular polygon; Orthodontics","routes":{"ca_aff":false,"ca_fund":false,"ca_venue":true,"about_ca":false,"invisible_to_affiliation_only":true},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.004451208,0.0006983971,0.0008435312,0.001453329,0.001001471,0.001822581,0.001054597,0.0009120848,0.002510949],"category_scores_gemma":[0.005662926,0.0003880585,0.001492457,0.001010777,0.002922423,0.003269116,0.002259268,0.003110207,0.0003918197],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00108317,"about_ca_system_score_gemma":0.0009716859,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0009879133,"about_ca_topic_score_gemma":0.001022942,"domain_scores_codex":[0.9982001,0.0004997582,0.0001906458,0.0003796545,0.0006262761,0.0001036246],"domain_scores_gemma":[0.9984934,0.0006691731,0.0001041794,0.0001618132,0.0004655563,0.0001058974],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","study_design_scores_codex":[0.00000677995,0.00001045132,0.0001469081,0.00003487672,0.000008708203,0.0001117118,0.0001280176,0.00294342,0.001074044,0.9857008,0.0005192908,0.009314963],"study_design_scores_gemma":[0.00001280508,0.00003040002,0.0002248954,0.00003115705,0.00001348158,0.0003128835,0.00005136077,0.07701863,0.001429095,0.9112737,0.009579044,0.0000225757],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"methods","genre_scores_codex":[0.01177496,0.0008972788,0.9745442,0.0003764244,0.0002147247,0.00006480468,0.00006791867,0.00004499047,0.01201472],"genre_scores_gemma":[0.3703099,0.002521838,0.6109822,0.0005510299,0.0004652934,0.0004804007,0.0001701832,0.0002188902,0.01430026],"genre_candidate":"methods","genre_consensus":"methods","teacher_disagreement_score":0.004451208,"threshold_uncertainty_score":0.02354056,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.007807725067741243,"score_gpt":0.2367515569242589,"score_spread":0.2289438318565176,"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."}}