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With respect to issue one, it can be simpler to consider the case where the constraint on the expected return is an equality. In that case, the first problem can be transformed to Minimize with respect to $\left\{ x,\lambda_{1},\lambda_{2}\right\} $: $x'\Sigma x + \lambda_{1} (\mu'x - r) + \lambda_{2} (1'x - 1)$ by the technique of Lagrangian multipliers, ...



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