English

On the geometry of sharp minima

Optimization and Control 2026-05-26 v1

Abstract

We give characterizations of sharp minimizers that emphasize their geometric properties. These include tilt invariance and weak upper gradient conditions. We relate sharp minimality to cusps in nonsmooth manifolds when interpreted locally as graphs and connect the rolling of tangent planes to the tilting of functions.

Keywords

Cite

@article{arxiv.2605.24766,
  title  = {On the geometry of sharp minima},
  author = {Alberto Domínguez Corella},
  journal= {arXiv preprint arXiv:2605.24766},
  year   = {2026}
}
R2 v1 2026-07-22T07:30:25.538Z