Abstract

We extend some recent developments on metric regularity in convex semi-infinite optimization from the case of a compact metric index set (for the constraint system) to the case of a compact Hausdorff one. The latter is the continuous setting where different contributions on stability in semi-infinite programming were developed since the 1980s (see for instance [1], [7] and [8]). In contrast, [3] and [4] (see also [2] for the linear case) deal with a compact metric index set when analysing the stable behaviour of KKT conditions. The fact of removing the ‘metric’ assumption yields some technical difficulties which are tackled in the present article via basic topological tools.