Minimization of an interval quadratic function in a Hilbert space

The problem of finding the minimum of a quadratic function with interval coefficients is considered. The concept of a $p$-universal solution to this problem is offered. The existence and uniqueness of $p$-universal solutions to the interval problem of minimization of a quadratic function is proved, an algorithm for finding them and their comparison are presented. As an application of the results the interval boundary value problem for the Poisson equation is examined.