Jb. Hiriart-urruty et As. Lewis, The Clarke and Michel-Penot subdifferentials of the eigenvalues of a symmetric matrix, COMPUT OP A, 13(1-3), 1999, pp. 13-23
We calculate the Clarke and Michel-Penot subdifferentials of the function w
hich maps a symmetric matrix to its mth largest eigenvalue. We show these t
wo subdifferentials coincide, and are identical for all choices of index m
corresponding to equal eigenvalues. Our approach is via the generalized dir
ectional derivatives of the eigenvalue function, thereby completing earlier
studies on the classical directional derivative.