{"id":"W1536462627","doi":"10.1007/978-1-4419-9569-8_2","title":"Self-Dual Smooth Approximations of Convex Functions via the Proximal Average","year":2011,"lang":"en","type":"book-chapter","venue":"Springer optimization and its applications","topic":"Optimization and Variational Analysis","field":"Computer Science","cited_by":7,"is_retracted":false,"has_abstract":false,"ca_institutions":"Okanagan University College; University of British Columbia, Okanagan Campus; University of British Columbia","funders":"","keywords":"Smoothing; Dual (grammatical number); Operator (biology); Mathematics; Regular polygon; Duality (order theory); Convex analysis; Norm (philosophy); Convex function; Pure mathematics; Convex optimization; Geometry; Statistics","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":["metaepi_narrow"],"consensus_categories":[],"category_scores_codex":[0.0002301909,0.0003196277,0.0003356855,0.0003258138,0.0005323392,0.0001399702,0.0005436583,0.000228134,0.0006641133],"category_scores_gemma":[0.00001822383,0.0002693476,0.000159437,0.000358798,0.00009912614,0.0003937844,0.0002598735,0.0002642341,0.0001063363],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00004658107,"about_ca_system_score_gemma":0.0001608302,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000005936447,"about_ca_topic_score_gemma":0.000003799713,"domain_scores_codex":[0.998187,0.00003557864,0.0006471004,0.0005758667,0.0003657737,0.0001886487],"domain_scores_gemma":[0.9976837,0.000110467,0.0006170004,0.000773326,0.0006893137,0.0001261985],"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":[0.000002161508,0.00009260503,0.000003917844,0.00004685443,0.0001585624,2.039872e-7,0.0003116651,0.02916658,0.00000808294,0.9682533,0.0001971667,0.001758862],"study_design_scores_gemma":[0.0002760687,0.00003608561,0.00003960736,0.00002335586,0.0002468594,0.000009654408,0.00001035806,0.8612865,0.00004587179,0.008950989,0.1286533,0.0004213772],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":null,"genre_codex":"methods","genre_gemma":"methods","genre_scores_codex":[5.590653e-7,0.0003423848,0.8653781,0.0009873024,0.00007418037,0.0009310908,0.00005592488,0.0002077097,0.1320227],"genre_scores_gemma":[0.02460381,0.005307964,0.5932653,0.001358859,0.0006220132,0.001762665,0.001189318,0.0002383225,0.3716518],"genre_candidate":"methods","genre_consensus":"methods","teacher_disagreement_score":0.9593024,"threshold_uncertainty_score":0.9999759,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.01509841070359019,"score_gpt":0.2054201888036508,"score_spread":0.1903217781000606,"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."}}