strong semismoothness – Optimization Online

Nonsmooth Matrix Valued Functions Defined by Singular Values

Published: 2003/01/21

Complementarity and Variational Inequalities, Linear, Cone and Semidefinite Programming, Nonsmooth Optimization fischer-burmeister function, inverse singular value problem, strong semismoothness, svd

A class of matrix valued functions defined by singular values of nonsymmetric matrices is shown to have many properties analogous to matrix valued functions defined by eigenvalues of symmetric matrices. In particular, the (smoothed) matrix valued Fischer-Burmeister function is proved to be strongly semismooth everywhere. This result is also used to show the strong semismoothness … Read more

Strong semismoothness of eigenvalues of symmetric matrices and its application to inverse eigenvalue problems

Published: 2001/09/27

Jie Sun

Defeng Sun

Control Applications, Nonsmooth Optimization eigenvalues, inverse eigenvalue problems, newton's methods, quadratic convergence, strong semismoothness, symmetric matrices

It is well known that the eigenvalues of a real symmetric matrix are not everywhere differentiable. A classical result of Ky Fan states that each eigenvalue of a symmetric matrix is the difference of two convex functions. This directly implies that the eigenvalues of a symmetric matrix are semismooth everywhere. Based on a very recent … Read more