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In this work, we study an uncertain quadratic optimization problem by using the concept of stability radius. That allows to prove robustness of uncertain quadratic optimization models. Firstly, we determine the stability radius of this problem by applying Ascoli formula. Secondly, we show that its robust counterpart has at least an optimal solution. Finally, we deal with an application and provide some numerical methods for such an uncertain quadratic optimization problem. [ABSTRACT FROM AUTHOR]