J. Vicente Pérez
In this talk, we establish, under a suitable regularity condition, an exact conic relaxation for conic minimax convex polynomial optimization problems. We also consider a general conic minimax ρ-convex polynomial optimization problem, showing that a KKT condition at a global minimizer is necessary and sufficient for ensuring an exact relaxation with attainment of the coni programming relaxation.
Furthermore, we show that a parametric robust convex polynomial problem with convex compact uncertainty sets enjoys stable exact conic relaxations under the validation of a characteristic cone constraint qualification. Such relaxations become (1) stable exact semidefinite programming relaxations for a parametric robust SOS-convex polynomial problem, where the uncertainty sets are assumed to be bounded spectrahedral, and (2) stable exact second-order cone programming relaxations for some classes of parametric robust convex quadratic programs under ellipsoidal uncertainty sets.
Palabras clave: Conic programming, convex polynomial, exact relaxation
Programado
Optimización Continua II
10 de junio de 2025 15:30
MR 3