Abstract

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.

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