Solution Existence for Time-Varying Infinite Horizon Quadratic Programming

We consider a general, time-varying, infinite horizon, pure quadratic programming problem with positive-definite cost matrices and unbounded decision variables. Sufficient conditions are provided for there to exist an optimal solution. Specifically, we show that if the eigenvalues of the cost matrices are bounded away from zero, then a (unique) optimal solution exists. We apply our results to the infinite horizon LQ tracker problem in optimal control theory,