The second-order directional derivatives of singular values
Liwei Zhang, Xiantao Xiao, Ning ZHANG · Scientia Sinica Mathematica · 2013
This paper derives the formula for the second-order derivative of any singular value function in a direct way. As applications, the speci c expressions of the tangent cones and the second order tangent sets for the epigraphs of spectral norm and nuclear norm are established, which play important roles in the study of the rst and the second-order optimality conditions for matrix optimization.