VU-smoothness and proximal point results for some nonconvex functions
This article is concerned with a function f having a primal-dual gradient structure at a point (x) over bar which satisfies a property called strong transversality. The structure is related to VU-space decomposition, depending on the subdifferential of fat at (x) over bar. It is shown that there exists a C-2 primal track leading to (x) over bar and a space decomposition mapping that is C-1. As a result, there exists a second-order expansion of f on the primal track, an associated subdifferemial that is C-1 in a certain sense, and a corresponding dual track. For (x) over bar a minimizer, conditions on f are given to ensure that for any point near (x) over bar its corresponding proximal point is on the primal track.
proximal point vu-decomposition second-order derivatives