{"id":"W4391103088","doi":"10.3390/math12020352","title":"The Augmented Weak Sharpness of Solution Sets in Equilibrium Problems","year":2024,"lang":"en","type":"article","venue":"Mathematics","topic":"Optimization and Variational Analysis","field":"Computer Science","cited_by":1,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Alberta","funders":"Natural Science Foundation of Shandong Province; Natural Sciences and Engineering Research Council of Canada; National Natural Science Foundation of China; University of Alberta","keywords":"Mathematical optimization; Degenerate energy levels; Degeneracy (biology); Solution set; Solution concept; Premise; Variational inequality; Mathematics; Set (abstract data type); Finite set; Regular polygon; Optimization problem; Computer science; Applied mathematics; Mathematical analysis; Physics","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":[0.006202894,0.001286976,0.001531965,0.002198075,0.001293457,0.003383698,0.002039579,0.002050123,0.005203586],"category_scores_gemma":[0.03136519,0.0008530811,0.002332886,0.0009202759,0.004728887,0.006520785,0.004012585,0.005113035,0.0007107998],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001541182,"about_ca_system_score_gemma":0.001423341,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0006625736,"about_ca_topic_score_gemma":0.0004277185,"domain_scores_codex":[0.9967506,0.001133604,0.0002199693,0.000752466,0.0007920816,0.0003513222],"domain_scores_gemma":[0.9847183,0.01120926,0.001382137,0.0008850419,0.001284425,0.0005208651],"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":[0.0001071809,0.00008969304,0.001600351,0.0003207091,0.00006474101,0.0002445114,0.0005846367,0.09674634,0.006350833,0.871794,0.0006218496,0.0214751],"study_design_scores_gemma":[0.00003082328,0.0001884304,0.0005124066,0.0001130192,0.0000309067,0.0001512771,0.0001747634,0.3282866,0.004114932,0.6640994,0.002258199,0.00003922586],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"other","genre_scores_codex":[0.03851563,0.0003541122,0.9547567,0.000324626,0.00003446994,0.00008549148,0.00007143435,0.00008624849,0.005771313],"genre_scores_gemma":[0.7512218,0.000733066,0.240773,0.000272399,0.0001113912,0.0004848871,0.0002276922,0.0001448236,0.006030891],"genre_candidate":"other","genre_consensus":null,"teacher_disagreement_score":0.006202894,"threshold_uncertainty_score":0.03280443,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02156666159529515,"score_gpt":0.2622413077359841,"score_spread":0.240674646140689,"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."}}