{"id":"W1995339711","doi":"10.1007/s10107-013-0666-8","title":"Computing the conjugate of convex piecewise linear-quadratic bivariate functions","year":2013,"lang":"en","type":"article","venue":"Mathematical Programming","topic":"Advanced Optimization Algorithms Research","field":"Mathematics","cited_by":10,"is_retracted":false,"has_abstract":false,"ca_institutions":"Okanagan University College; University of British Columbia, Okanagan Campus; University of British Columbia","funders":"","keywords":"Mathematics; Bivariate analysis; Piecewise; Regular polygon; Quadratic equation; Piecewise linear function; Applied mathematics; Convex analysis; Convex conjugate; Convex optimization; Proper convex function; Mathematical optimization; Mathematical analysis; Statistics; Geometry","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":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.001890358,0.0007271958,0.000962837,0.001100676,0.000433531,0.002520385,0.001075171,0.001079704,0.005505748],"category_scores_gemma":[0.01216727,0.0005453575,0.0005388152,0.001018232,0.001327816,0.002613374,0.002093467,0.001795698,0.0009633697],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001095964,"about_ca_system_score_gemma":0.001125001,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001054503,"about_ca_topic_score_gemma":0.001021932,"domain_scores_codex":[0.9993652,0.0002355206,0.00002571599,0.00008970594,0.0001977899,0.00008620011],"domain_scores_gemma":[0.9975476,0.001402744,0.0001863401,0.0002584102,0.0003893458,0.0002155956],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"simulation_or_modeling","study_design_gemma":"theoretical_or_conceptual","study_design_scores_codex":[0.0006430328,0.000179938,0.00328886,0.0002333633,0.00006965968,0.0002346353,0.0002716941,0.5691431,0.009598839,0.2658223,0.003531005,0.1469837],"study_design_scores_gemma":[0.0000127016,0.00006968321,0.0003736723,0.00001702322,0.00001116369,0.00006139869,0.00006913849,0.9446545,0.00418182,0.04966881,0.0008665246,0.00001356262],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":null,"genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.09329771,0.0001193941,0.9023368,0.0002402626,0.00006220706,0.00002532219,0.00007357328,0.0002674609,0.003577402],"genre_scores_gemma":[0.7852034,0.0002112698,0.2088541,0.00007918931,0.0000528683,0.000045639,0.0002500884,0.0003129241,0.00499058],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.005505748,"threshold_uncertainty_score":0.01841855,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.05572542173380636,"score_gpt":0.352413941868189,"score_spread":0.2966885201343826,"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."}}