  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 study the case of a multiobjective optimization
problem defined via m convex C^1,1 objective functions on a given closed ball
in R^n. Two approaches are proposed: the first one adopts a local point of view
around a given solution point, whereas the second one considers the solution
set as a whole. A comparison between the two notions of well-conditioned
problem is developed. We underline that both the condition numbers introduced
in the present work reduce to the same of condition number proposed by Zolezzi
in 2003, in the special case of the scalar optimization problem considered
there. A pseudodistance between functions is defined such that the condition
number provides an upper bound on how far from a well-conditioned function f a
perturbed function g can be chosen in order that g is well-conditioned too. For
both the local and the global approach an extension of classical Eckart-Young
distance theorem is proved, even if only a special class of perturbations is
considered.
