The Approximate Sum Rule For Proximal Subdifferential In Hilbert Spaces

In this thesis, we mainly study the proper, lower semi-continuous function’s ap-proximate sum rules for proxiaml subdifferential in Hilbert spaces. With the smooth variational principle in Hilbert spaces we establish a nonlocal approximate sum rule and a strong local approximate sum rule for proximal subdifferential. Finally, ap-plied them, we obtain a strong local approximate sum rule of Proximal-Coderivative for closed multifunction in Hilbert spaces.