{"id":"W2093605433","doi":"10.1007/s10107-006-0072-6","title":"Invariance and efficiency of convex representations","year":2006,"lang":"en","type":"article","venue":"Mathematical Programming","topic":"Advanced Optimization Algorithms Research","field":"Mathematics","cited_by":30,"is_retracted":false,"has_abstract":false,"ca_institutions":"University of Waterloo","funders":"","keywords":"Mathematics; Conic optimization; Dual cone and polar cone; Representation (politics); Regular polygon; Duality (order theory); Invariant (physics); Complementarity (molecular biology); Convex analysis; Convex set; Conic section; Path (computing); Smoothness; Convex hull; Convex optimization; Pure mathematics; Mathematical analysis; Computer science; Geometry","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":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.005080059,0.0008336771,0.001432367,0.001640998,0.0005910725,0.004192589,0.001944848,0.001070085,0.007051215],"category_scores_gemma":[0.03777514,0.0006960077,0.001113093,0.001948833,0.003585311,0.009247099,0.003631886,0.002999068,0.001468814],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001126746,"about_ca_system_score_gemma":0.0008187988,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0006266895,"about_ca_topic_score_gemma":0.0003265021,"domain_scores_codex":[0.9961559,0.00184691,0.000209525,0.0005146471,0.0008381071,0.0004348897],"domain_scores_gemma":[0.9791626,0.01308525,0.001193173,0.005076559,0.001034253,0.0004481498],"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":[0.0001886282,0.00006749725,0.000775632,0.00005893215,0.00003366632,0.00004872962,0.0001705367,0.02231785,0.002328096,0.9360707,0.001456631,0.03648301],"study_design_scores_gemma":[0.00002536096,0.00007021986,0.0005947942,0.00001478787,0.00001801169,0.00006156865,0.00006028057,0.09973019,0.002161809,0.8959538,0.001296584,0.0000127244],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.1696321,0.0008021332,0.7982449,0.001325293,0.00009443731,0.00006880427,0.0003008563,0.0003665492,0.02916485],"genre_scores_gemma":[0.9308661,0.0008794476,0.05834596,0.0002520967,0.0002018854,0.0001335892,0.0004740695,0.0005362841,0.008310651],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.007051215,"threshold_uncertainty_score":0.02686626,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.04243372711367955,"score_gpt":0.361508172300855,"score_spread":0.3190744451871754,"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."}}