The problem of minimizing &ftilde; = f + p over some convex subset of a Euclidean space is investigated, where f(x) = x
T
Ax
b
T
x is strictly convex and |p| is only assumed to be bounded by some positive number s. It is shown that the function &ftilde; is strictly outer γ-convex for any γ>
γ*, where γ* is determined by s and the smallest eigenvalue of A. As consequence, a γ*-local minimal solution of &ftilde; is its global minimal solution and the diameter of the set of global minimal solutions of &ftilde; is less than or equal to γ*. Especially, the distance between the global minimal solution of f and any global minimal solution of &ftilde; is less than or equal to γ*/2. This property is used to prove a roughly generalized support property of &ftilde; and some generalized optimality conditions.
