On partial smoothness, tilt stability and the $${\mathcal {VU}}$$-decomposition

Partial Smoothness, Tilt Stability, and Generalized Hessians

We compare two recent variational-analytic approaches to second-order conditions and sensitivity analysis for nonsmooth optimization. We describe a broad setting where computing the generalized Hessian of Mordukhovich is easy. In this setting, the idea of tilt stability introduced by Poliquin and Rockafellar is equivalent to a classical smooth second-order condition.

Tensor Decomposition with Smoothness

Tensor Decomposition with Smoothness

Real data tensors are typically high dimensional; however, their intrinsic information is preserved in low-dimensional space, which motivates the use of tensor decompositions such as Tucker decomposition. Frequently, real data tensors smooth in addition to being low dimensional, which implies that adjacent elements are similar or continuously changing. These elements typically appear as spatial...

On the Smoothness of Functors

In this paper we will try to introduce a good smoothness notion for a functor. We consider properties and conditions from geometry and algebraic geometry which we expect a smooth functor should has.

Smoothness , semi - stability and alterationsby