Global infimum of strictly convex quadratic functions with bounded perturbations

The problem of minimizing (f) over tilde= 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 (f) over tilde is strictly outer. gamma-convex for any gamma > gamma*, where gamma* is determined by s and the smallest eigenvalue of A. As consequence, a gamma*- local minimal solution of (f) over tilde is its global minimal solution and the diameter of the set of global minimal solutions of (f) over tilde is less than or equal to gamma*/2. Especially, the distance between the global minimal solution of f and any global minimal solution of (f) over tilde is less than or equal to gamma*/ 2. This property is used to prove a roughly generalized support property of (f) over tilde and some generalized optimality conditions.