Maximizing Strictly Convex Quadratic Functions with Bounded Perturbations

The problem of maximizing $\tilde{f}=f+p$ over some convex subset D of the n‐dimensional Euclidean space is investigated, where f is a strictly convex quadratic function and p is assumed to be bounded by some s∈[0,+∞[. The location of global maximal solutions of $\tilde{f}$ on D is derived from the roughly generalized convexity of $\tilde{f}$ . The distance between global (or local) maximal solutions of $\tilde{f}$ on D and global (or local, respectively) maximal solutions of f on D is estimated. As consequence, the set of global (or local) maximal solutions of $\tilde{f}$ on D is upper (or lower, respectively) semicontinuous when the upper bound s tends to zero.