New characterizations of Hoffman constants for systems of linear constraints

We give a characterization of the Hoffman constant of a system of linear constraints in $\R^n$ relative to a reference polyhedron $R\subseteq\R^n$. The reference polyhedron $R$ represents constraints that are easy to satisfy such as box constraints. In the special case $R = \R^n$, we obtain a novel characterization of the classical Hoffman constant. More … Read more

Uniform Laws of Large Numbers for Set-Valued Mappings and Subdifferentials of Random Functions

We derive a uniform (strong) Law of Large Numbers (LLN) for random set-valued mappings. The result can be viewed as an extension of both, a uniform LLN for random functions and LLN for random sets. We apply the established results to a consistency analysis of stationary points of sample average approximations of nonsmooth stochastic programs. … Read more

Weak Stationarity: Eliminating the Gap between Necessary and Sufficient Conditions

Starting from known necessary extremality conditions in terms of strict subdifferentials and normals the notion of weak stationarity is introduced. It is defined in terms of initial space elements. The necessary conditions become necessary and sufficient (for stationarity). Citation School of Information Technology and Mathematical Sciences, Centre of Information and Applied Optimization, University of Ballarat, … Read more