Differential Properties of the Symmetric Matrix‐Valued Fischer‐Burmeister Function

This paper focuses on the study of differential properties of the symmetric matrix‐valued Fischer–Burmeister (FB) function. As the main results, the formulas for the directional derivative, the B‐subdifferential and the generalized Jacobian of the symmetric matrix‐valued Fischer–Burmeister function are established, which can be utilized in designing implementable Newton‐type algorithms for nonsmooth equations involving the symmetric matrix‐valued FB function.