Error Bounds for a Class of Cone-Convex Inclusion Problems

Abstract: In this paper, we investigate error bounds for cone-convex inclusion problems in finite-dimensional settings of the form $f(x)\in K$, where $K$ is a smooth cone and $f$ is a continuously differentiable and $K$-concave function. We show that local error bounds for the inclusion can be characterized by the Abadie constraint qualification around the reference point. In the case where $f$ is an affine function, we precisely identify the conditions under which the inclusion admits global error bounds. Additionally, we derive some properties of smooth cones, as well as regular cones and strictly convex cones.