{"id":"W2593829505","doi":"10.1016/j.jat.2012.05.008","title":"Attouch–Théra duality revisited: Paramonotonicity and operator splitting","year":2012,"lang":"en","type":"article","venue":"Journal of Approximation Theory","topic":"Optimization and Variational Analysis","field":"Computer Science","cited_by":45,"is_retracted":false,"has_abstract":false,"ca_institutions":"University of British Columbia, Okanagan Campus; University of British Columbia","funders":"Natural Sciences and Engineering Research Council of Canada; University of British Columbia; Canada Research Chairs; Deutsche Forschungsgemeinschaft","keywords":"Mathematics; Duality (order theory); Monotone polygon; Hilbert space; Operator (biology); Intersection (aeronautics); Projection (relational algebra); Pure mathematics; Combinatorics; Applied mathematics; Discrete mathematics; Algorithm","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":"codex-gemma-dda1882f352a","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.00329965,0.00008411923,0.0001876145,0.00013249,0.0001209455,0.0001481053,0.0002250307,0.00004447205,0.00005407277],"category_scores_gemma":[0.0003254058,0.00006578962,0.00007780216,0.0002935941,0.00002608729,0.001537655,0.00007214955,0.000126735,0.000009744213],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0000392575,"about_ca_system_score_gemma":0.00003998669,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":8.704551e-7,"about_ca_topic_score_gemma":5.599995e-8,"domain_scores_codex":[0.9987155,0.0003119805,0.0004694284,0.00009870398,0.0002712765,0.0001331469],"domain_scores_gemma":[0.9987273,0.0002018809,0.0004993625,0.0001623622,0.0002787509,0.0001303608],"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":[0.00001887738,0.000121942,0.004651577,0.00002532256,0.0000705738,8.583639e-7,0.001528129,0.0007728664,0.0002717399,0.9835004,0.000211625,0.008826099],"study_design_scores_gemma":[0.002785127,0.0002429703,0.1064678,0.0002218609,0.0003279291,0.0004705035,0.001217957,0.6701162,0.007123676,0.2013399,0.008686258,0.000999833],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":null,"genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.06824346,0.0003925511,0.9292504,0.000957687,0.0001174706,0.00006680044,0.000001245908,0.00001987794,0.0009504754],"genre_scores_gemma":[0.8528088,0.00005164984,0.1463567,0.0005252872,0.0001726553,0.00000152595,0.000001719144,0.000004330447,0.0000772673],"genre_candidate":"methods","genre_consensus":null,"teacher_disagreement_score":0.7845653,"threshold_uncertainty_score":0.2682823,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.01264066668480964,"score_gpt":0.2530446148449361,"score_spread":0.2404039481601265,"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."}}