Conic relaxations for classes of convex polynomial programs

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.

Keywords: Conic programming, convex polynomial, exact relaxation

Continuous Optimization II
June 10, 2025  3:30 PM
MR 3

J. Castro Pérez, L. F. Escudero Bueno, J. F. Monge Ivars

J. Rückmann

X. Moreno-Vassart, F. J. Toledo, V. Herranz, V. Galiano

M. Rodríguez Álvarez, J. Vicente Pérez, J. E. Martínez Legaz