Continuity properties in semi-infinite parametric linear optimization

In this paper, we treat optimization problems of the following type: minimize a linear functional p on a closed, convex subset of Euclidean m-space. (Semi- infinite linear optimization problems are of this type.) We investigate upper semicontinuity of the set of optimal solutions and the continuous dependence of the optimal value on p. Thereby we essentially work with the concept of characteristic cones of closed, convex sets.