TL;DR
This paper studies a class of sublinear functionals called gauge functions that characterize the interior and exterior of convex cones in normed linear spaces, providing a mathematical framework for cone analysis.
Contribution
It introduces and analyzes gauge functions as tools to describe the interior and exterior of convex cones in normed spaces, offering new insights into cone characterization.
Findings
Gauge functions effectively characterize cone interiors.
They provide a dual perspective on convex cone boundaries.
The framework applies to various normed linear spaces.
Abstract
We analyze a class of sublinear functionals which characterize the interior and the exterior of a convex cone in a normed linear space.
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Taxonomy
TopicsOptimization and Variational Analysis · Functional Equations Stability Results · Advanced Optimization Algorithms Research