Strong Lagrangian duality holds for the quadratic programming with a two-sided quadratic constraint. In this paper, we show that the two-sided quadratic constrained quadratic fractional programming, if well scaled, also has zero Lagrangian duality gap. However, this is not always true without scaling. For a special case, the identical regularized total least squares problem, we establish the necessary and sufficient condition under which the Lagrangian duality gap is positive.

中文翻译：

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具有双面二次约束的二次分数阶规划的拉格朗日对偶间隙

强拉格朗日对偶性适用于带有两边二次约束的二次规划。在本文中，我们证明了双面二次约束二次分数阶规划，如果缩放比例合理，则也具有零拉格朗日对偶间隙。但是，如果不进行缩放，情况并非总是如此。对于一个特例，相同的正则化总最小二乘问题，我们建立了拉格朗日对偶间隙为正的充要条件。