Some results on condition numbers in convex multiobjective optimization

Abstract Various notions of condition numbers are used to study some sensitivity aspects of scalar optimization problems. The aim of this paper is to introduce a notion of condition number to treat the case of a multiobjective optimization problem defined via m convex C^{1,1} objective functions on a given closed ball in \mathbb{R}^{n}. Two approaches are proposed: the first one adopts a local point of view around a solution point, whereas the second one considers the solution set as a whole. We underline that, in the scalar case, both of them reduce to the condition number proposed by Zolezzi. Extensions of the Eckart--Young distance theorem are proved in both cases.