Why is the first order condition for $f$ is $f(\mathbf y) \ge f(\mathbf x)+2Re\{\nabla f(\mathbf x)^T(\mathbf y-\mathbf x)\} ? $
According to the first order condition in optimization : $g(\mathbf y) \ge g(\mathbf x)+ \nabla g(\mathbf x)^T(\mathbf y-\mathbf x)$,why is there a $2Re\{\}$ in the first formula? There is just a hint said that let $ \mathbf x =\mathbf x_r+j\mathbf x_i $
