On Certain Properties of Convex Functions
Miel Sharf, Daniel Zelazo
TL;DR
This paper explores specific properties of convex functions, including the convexity of their minima set, subgradient behavior under restrictions, and optimization over affine subspaces.
Contribution
It presents new theoretical results on the structure and optimization characteristics of convex functions.
Findings
Convexity of the set of minima is established.
Subgradient sets behave predictably under restrictions.
Optimization over affine subspaces is characterized.
Abstract
This note deals with certain properties of convex functions. We provide results on the convexity of the set of minima of these functions, the behaviour of their subgradient set under restriction, and optimization of these functions over an affine subspace.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsOptimization and Variational Analysis · Mathematical Inequalities and Applications · Analytic and geometric function theory