  In this paper, we solve a maximization problem where the objective function
is quadratic and convex or concave and the constraints set is the reachable
value set of a convergent discrete-time affine system. Moreover, we assume that
the matrix defining the system is diagonalizable. The difficulty of the problem
lies in the infinite sequence to handle in the constraint set. Equivalently,
the problem requires to solve an infinite number of quadratic programs.
Therefore, the main idea is to extract a finite of them and to guarantee that
the resolution of the extracted problems provides the optimal value and a
maximizer for the initial problem. The number of quadratic programs to solve
has to be the smallest possible. Actually, we construct a family of integers
that over-approximate the exact number of quadratic programs to solve using
basic ideas of linear algebra. This family of integers is used in the final
algorithm. A new computation of an integer of the family within the algorithm
ensures a reduction of the number of loop iterations. The method proposed in
the paper is illustrated on small academic examples. Finally, the algorithm is
experimented on randomly generated instances of the problem.

Optimization and Control