Stability of Pareto-optimal vectorial estimates and $\varepsilon$-equilibrium solutions

A definition is given of stability for a set of Pareto optimal vectorial estimates. The necessary and sufficient stability conditions are fomulated in terms of continuity of a multi-valued mapping which is closely related with notions of $\varepsilon$-equilibrium vectorial optimization. A regularization scheme is given which permits transforming the unstable problem of multi-criterial optimization into its kindred problem which is almost surely stable.