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

Abstract

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.

Complementarity problems with respect to Loewnerian cones

“…An explicit formula for computing the Clarke subdifferential of κ fb can be found in [28]. If the matrix X 2 t + Y 2 t is nonsingular, then Lemma 2.2 yields…”

“…Consider the general complementarity problem (5) with K being a Loewnerian cone induced by F. Thanks to the duality formula (28) and the fact that…”