No Gap Second-order Optimality Conditions for a Matrix Cone Programming Induced by the Nuclear Norm
Ning Zhang, Liwei Zhang · Asia Pacific Journal of Operational Research · 2016
The first-order and the second-order directional derivatives of singular values are used to characterize the tangent cone, the normal cone and the second-order tangent set of the epigraph of the nuclear norm of matrices. Based on the variational geometry of the epigraph, the no gap second-order optimality conditions for the optimization problem, whose constraint is defined by the matrix cone induced by the nuclear norm, are established.