{"id":"W4410527853","doi":"10.23952/jnva.9.2025.5.08","title":"Image space analysis to lagrange duality in nonconvex set optimization","year":2025,"lang":"en","type":"article","venue":"Journal of Nonlinear and Variational Analysis","topic":"Optimization and Variational Analysis","field":"Computer Science","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"Fundamental Research Funds for the Central Universities; National Natural Science Foundation of China","keywords":"Duality (order theory); Space (punctuation); Set (abstract data type); Mathematics; Image (mathematics); Lagrange multiplier; Mathematical optimization; Computer science; Combinatorics; Artificial intelligence; Programming language","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":"codex-gemma-dda1882f352a","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.001373564,0.0001598748,0.0006188246,0.003826228,0.0001158608,0.0002570872,0.0004115591,0.00008383353,0.0002002585],"category_scores_gemma":[0.000304217,0.0001407497,0.000477156,0.01328912,0.00002041701,0.0006588873,0.0001244395,0.0001581361,0.000004478638],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0001010147,"about_ca_system_score_gemma":0.0001917602,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0001708292,"about_ca_topic_score_gemma":0.0002052508,"domain_scores_codex":[0.997871,0.0002185407,0.0008823705,0.0003239527,0.0005355203,0.0001685611],"domain_scores_gemma":[0.9978775,0.0002932049,0.0004477731,0.0002613913,0.0009734006,0.000146758],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"simulation_or_modeling","study_design_gemma":"simulation_or_modeling","study_design_scores_codex":[0.00003254584,0.0001721457,0.03855484,0.000007825824,0.004681803,0.000007074587,0.0003652114,0.9411299,0.00003620939,0.01464467,0.0001258634,0.0002419337],"study_design_scores_gemma":[0.000397126,0.00002288388,0.1464662,0.000006410621,0.00242572,0.000001606827,0.00004212857,0.8496308,0.00001081039,0.0006022767,0.0002757894,0.0001182482],"study_design_candidate":"simulation_or_modeling","study_design_consensus":"simulation_or_modeling","genre_codex":"methods","genre_gemma":"methods","genre_scores_codex":[0.004421853,0.00006384516,0.9826115,0.01228953,0.00007099193,0.00006605528,0.000030994,0.00001294154,0.0004323004],"genre_scores_gemma":[0.2325759,0.0001016004,0.7654265,0.001296335,0.0001007825,0.000003999638,0.00008963799,0.000005079216,0.0004002751],"genre_candidate":"methods","genre_consensus":"methods","teacher_disagreement_score":0.228154,"threshold_uncertainty_score":0.6384981,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.01021147103694714,"score_gpt":0.2897130009053495,"score_spread":0.2795015298684023,"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."}}