{"id":"W4318332842","doi":"10.23952/jano.5.2023.1.05","title":"Convexity and continuity of specific set-valued maps and their extremal value functions","year":2023,"lang":"en","type":"article","venue":"Journal of Applied and Numerical Optimization","topic":"Optimization and Variational Analysis","field":"Computer Science","cited_by":1,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"Deutsche Forschungsgemeinschaft","keywords":"Convexity; Mathematics; Set (abstract data type); Value (mathematics); Combinatorics; Applied mathematics; Statistics; Computer science; Economics; Financial economics","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":[0.003309026,0.000915019,0.001183903,0.002286216,0.0008997696,0.003645334,0.001146723,0.001342719,0.002177805],"category_scores_gemma":[0.01336202,0.0005927512,0.001167865,0.001303637,0.003331195,0.005047667,0.001927084,0.002740495,0.0002976768],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001544536,"about_ca_system_score_gemma":0.0007202053,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0005039121,"about_ca_topic_score_gemma":0.0003321664,"domain_scores_codex":[0.9987055,0.0004460691,0.00007225788,0.0002879137,0.0003373298,0.0001509358],"domain_scores_gemma":[0.9944198,0.003543589,0.0006122689,0.0003079647,0.0007735037,0.0003429231],"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":[0.00005521745,0.00004051431,0.001151379,0.0002261666,0.00006360588,0.0003358261,0.0002731624,0.04464512,0.003580775,0.9335473,0.0009659724,0.01511488],"study_design_scores_gemma":[0.00001182841,0.00006567025,0.001677735,0.000116807,0.00003414754,0.0004788595,0.0002010079,0.2463963,0.003116434,0.7443702,0.003489924,0.00004107965],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.1371184,0.002425823,0.8330597,0.001220802,0.0001009975,0.00009327636,0.0003217628,0.0001146741,0.02554464],"genre_scores_gemma":[0.8904349,0.002312143,0.1005705,0.000176748,0.0001913421,0.000247626,0.0003275315,0.0001724386,0.005566677],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.003645334,"threshold_uncertainty_score":0.01750004,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.01607627434821768,"score_gpt":0.2236571073834695,"score_spread":0.2075808330352518,"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."}}