Smoothness, semi-stability and alterations

Smoothness , semi - stability and alterationsby

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.

Graph-based Semi-supervised Learning: Realizing Pointwise Smoothness Probabilistically

As the central notion in semi-supervised learning, smoothness is often realized on a graph representation of the data. In this paper, we study two complementary dimensions of smoothness: its pointwise nature and probabilistic modeling. While no existing graph-based work exploits them in conjunction, we encompass both in a novel framework of Probabilistic Graph-based Pointwise Smoothness (PGP), ...

Semi Stability Factors

A (semistability) factor [semifactor] of a matrix AE r: nn is a positive definite [positive semidefinite] matrix H such that AH + HA* is positive semidefinite. We give three proofs to show that if A has a semistability factor then it cannot be unique. We give necessary and sufficient conditions for a matrix H to be a (semi)factor of a given matrix. We also determine the dimension of the cone of...

Control-Theoretic Analysis of Smoothness for Stability-Certified Reinforcement Learning

It is critical to obtain stability certificate before deploying reinforcement learning in real-world mission-critical systems. This study justifies the intuition that smoothness (i.e., small changes in inputs lead to small changes in outputs) is an important property for stability-certified reinforcement learning from a control-theoretic perspective. The smoothness margin can be obtained by sol...