jats:pWe analyze the optimality of the stable fixed point of the double-bracket equations. We introduce different types of optimality and prove local and global optimality results with respect to the Schatten<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="$p$" id="E1">mml:mip</mml:mi></mml:math>-norms.</jats:p>