{"id":"W4407244990","doi":"10.1007/s11590-025-02192-7","title":"A necessary condition for the guarantee of the superiorization method","year":2025,"lang":"en","type":"article","venue":"Optimization Letters","topic":"Optimization and Variational Analysis","field":"Computer Science","cited_by":1,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Waterloo","funders":"Natural Sciences and Engineering Research Council of Canada; National Cancer Institute; National Institutes of Health; University of Haifa; Israel Science Foundation; National Natural Science Foundation of China; Deutsches Krebsforschungszentrum","keywords":"Iterated function; Sequence (biology); Function (biology); Outcome (game theory); Mathematics; Mathematical optimization; Value (mathematics); Convergence (economics); Initial value problem; Convex function; Rate of convergence; Regular polygon; Algorithm; Gradient descent; Applied mathematics; Computer science; Mathematical economics; Statistics; Mathematical analysis; Channel (broadcasting); Artificial intelligence","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":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.006786149,0.001584046,0.001536717,0.0009571908,0.001440829,0.001604293,0.001857246,0.002438681,0.007597808],"category_scores_gemma":[0.05333082,0.0007911096,0.001346727,0.0005673268,0.00478438,0.004120343,0.004735879,0.005007647,0.00162232],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001116041,"about_ca_system_score_gemma":0.0031654,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001077014,"about_ca_topic_score_gemma":0.0004984282,"domain_scores_codex":[0.9958674,0.001205205,0.0002391724,0.0009302038,0.001176807,0.0005811504],"domain_scores_gemma":[0.966832,0.02198217,0.00280828,0.002425772,0.004664549,0.001287222],"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":[0.0005343726,0.0001448495,0.002637642,0.0006688047,0.0001037249,0.0004730913,0.0005893468,0.1954885,0.02714691,0.73545,0.005671448,0.03109125],"study_design_scores_gemma":[0.0001050875,0.0006129936,0.0007970629,0.0001651394,0.00003610072,0.0004624269,0.0001185314,0.7402276,0.01508269,0.2364089,0.005910231,0.00007321878],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"methods","genre_scores_codex":[0.04242849,0.0004945784,0.9348804,0.002004622,0.0001657171,0.0001445325,0.0001916315,0.0005661692,0.01912398],"genre_scores_gemma":[0.8059445,0.0008246013,0.1828462,0.001076963,0.0004121399,0.0007352915,0.0004369454,0.0007274178,0.006995941],"genre_candidate":"methods","genre_consensus":"methods","teacher_disagreement_score":0.007597808,"threshold_uncertainty_score":0.03588903,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.006837686961980912,"score_gpt":0.2661051495676065,"score_spread":0.2592674626056256,"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."}}