{"id":"W2061220204","doi":"10.1287/moor.1060.0219","title":"Constraint Qualifications and KKT Conditions for Bilevel Programming Problems","year":2006,"lang":"en","type":"article","venue":"Mathematics of Operations Research","topic":"Optimization and Variational Analysis","field":"Computer Science","cited_by":66,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Victoria","funders":"","keywords":"Karush–Kuhn–Tucker conditions; Constraint (computer-aided design); Mathematics; Bilevel optimization; Mathematical optimization; Constraint programming; Constraint logic programming; Constraint satisfaction; Binary constraint; Set (abstract data type); Nonlinear programming; Sequence (biology); Optimization problem; Nonlinear system; Computer science; Stochastic programming","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":[0.004803509,0.001242381,0.001526561,0.0009829946,0.001374659,0.002692245,0.001239978,0.002036701,0.009382006],"category_scores_gemma":[0.01572519,0.000742487,0.00109557,0.00200107,0.004182826,0.004622371,0.002944018,0.004073285,0.002088724],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001686354,"about_ca_system_score_gemma":0.003021754,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.003063136,"about_ca_topic_score_gemma":0.002049115,"domain_scores_codex":[0.9958059,0.001781704,0.0003182229,0.0006517646,0.001026376,0.0004160086],"domain_scores_gemma":[0.9945781,0.003156047,0.0006142842,0.0003529883,0.001060763,0.0002377725],"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":[0.00001773509,0.00002151051,0.0001677556,0.0001550614,0.0000160537,0.0001456661,0.0001386183,0.04942535,0.0004510759,0.9377631,0.00249299,0.009205077],"study_design_scores_gemma":[0.0000250263,0.00003342373,0.0001534421,0.00008631097,0.000007929737,0.00007087853,0.00009351693,0.1221141,0.0004252497,0.8684593,0.008504531,0.00002620283],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.00910328,0.0006640374,0.9565957,0.002001996,0.0001844083,0.0001143049,0.0004626612,0.00009062938,0.03078299],"genre_scores_gemma":[0.5322267,0.004450012,0.4363115,0.001509443,0.0006614813,0.001490723,0.001994222,0.000255898,0.02110009],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.009382006,"threshold_uncertainty_score":0.03138596,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.1242592753038148,"score_gpt":0.4028250776607806,"score_spread":0.2785658023569658,"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."}}