𝒱𝒰-smoothness and proximal point results for some nonconvex functions
Robert B. Mifflin, Claudia A. Sagastizábal · Optimization methods & software · 2004
This article is concerned with a function f having a primal–dual gradient structure at a point x¯ which satisfies a property called strong transversality. The structure is related to 𝒱𝒰-space decomposition, depending on the subdifferential of f at x¯. It is shown that there exists a C 2 primal track leading to x¯ 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 subdifferential that is C 1 in a certain sense, and a corresponding dual track. For x¯ a minimizer, conditions on f are given to ensure that for any point near x¯ its corresponding proximal point is on the primal track.