Global stability of interval optimization problems

Abstract

We study the global stability of interval optimization problems and focus on set-type solutions that are defined by means of the Kulisch–Miranker order between intervals. In order to carry out this, we employ a variational convergence notion for vector functions taken from the literature and provide geometric and metric characterizations of this variational convergence for interval functions. We describe the global behaviour of the solution, level and colevel sets under variations of the data and show that the coercivity and coercive existence conditions for these problems are preserved locally within certain classes of functions. Then, we compare the variational convergence with other convergence notions taken from the literature. Finally, we study the behaviour of the operations with interval functions under variations of the data.