{"id":"W4401486906","doi":"10.37256/cm.5320243986","title":"Theorem of Alternative and Scalarization of Optimization Problems in Topological Vector Spaces","year":2024,"lang":"en","type":"article","venue":"Contemporary Mathematics","topic":"Advanced Theoretical and Applied Studies in Material Sciences and Geometry","field":"Engineering","cited_by":2,"is_retracted":false,"has_abstract":true,"ca_institutions":"Saskatchewan Polytechnic","funders":"","keywords":"Mathematics; Locally convex topological vector space; Topological vector space; Vector optimization; Pure mathematics; Topological space; Topology (electrical circuits); Algebra over a field; Optimization problem; Mathematical optimization; Combinatorics","routes":{"ca_aff":true,"ca_fund":false,"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":[0.0001308872,0.00005738093,0.0001463337,0.00004080334,0.000008956654,0.00001070087,0.00004705759,0.00002937226,0.00002042891],"category_scores_gemma":[0.00002595009,0.00003968065,0.00001294372,0.0001649903,0.0001548108,0.00006115637,0.00002802683,0.00003485767,3.867296e-7],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.000005116402,"about_ca_system_score_gemma":0.00000310497,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000001379584,"about_ca_topic_score_gemma":2.589677e-7,"domain_scores_codex":[0.9996164,0.000007388214,0.0001901251,0.00006729402,0.00006310463,0.00005567553],"domain_scores_gemma":[0.999818,0.00008975529,0.00002418363,0.00004211752,0.00001208864,0.00001380234],"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":[0.000003836251,0.00003211394,0.0001032655,0.001041097,0.00001773415,0.000001467574,0.001978816,0.1240184,0.002729956,0.8693808,0.00001314827,0.0006793397],"study_design_scores_gemma":[0.0001112909,0.00006576555,0.00003563026,0.0003641435,0.000005109773,0.000001099118,0.0006965575,0.5726584,0.00663667,0.4192423,0.00008890504,0.00009421675],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":null,"genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.1965083,0.002398265,0.7783928,0.00008932602,0.0002429123,0.0002708341,0.00001640996,0.00007367656,0.02200751],"genre_scores_gemma":[0.9932291,0.0002063749,0.006521964,0.000001697116,0.00001355383,0.000005185075,0.000001836505,0.000004859651,0.00001544704],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.7967208,"threshold_uncertainty_score":0.161813,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.01586885348927385,"score_gpt":0.2380359524716049,"score_spread":0.2221670989823311,"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."}}