A Weak Sum Rule And A Chain Rule For Proximal Subdifferential In Hilbert Spaces

The sum rules and chain rules for subdifferential are important theorems in nonsmooth analysis. In this thesis we discuss a weak sum rule for proximal subd-ifferential of several lower semicontinuous functionals and a chain rule for proximal subdifferential of two lower semicontinuous functionals in Hilbert spaces, we estab-lish a weak sum rule and a chain rule for proximal coderivative of closed multifunc-tions in Hilbert spaces.