
TL;DR
This paper investigates the extension of convex functions from non-convex domains to their convex hulls, analyzing both local and global convexity, including cases defined by positive definite Hessians.
Contribution
It provides new theoretical results on extending convex functions and convexity defined by positive definite Hessians beyond their original domains.
Findings
Characterization of conditions for extending convex functions
Extension results for convex functions with positive definite Hessians
Parallel results for local and global convexity
Abstract
We study the local and global versions of the convexity, which is closely related to the problem of extending a convex function on a non-convex domain to a convex function on the convex hull of the domain and beyond the convex hull. We also give the parallel results for the convexity defined by positive definite Hessian.
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Taxonomy
TopicsOptimization and Variational Analysis · Mathematical Inequalities and Applications · Advanced Optimization Algorithms Research
