Intrinsic perturbation scale for certified oracle objectives with epigraphic information
We introduce a natural displacement control for minimizer sets of oracle objectives equipped with certified epigraphic information. Formally, we replace the usual local uniform value control of objective perturbations - uncertifiable from finite pointwise information without additional structure - by the strictly weaker requirement of a cylinder-localized vertical epigraphic control, naturally provided by certified envelopes. Under set-based quadratic growth (allowing nonunique minimizers), this yields the classical square-root displacement estimate with optimal exponent 1/2, without any extrinsic assumption.
| Authors | Karim Bounja, Boujemaâ Achchab, Abdeljalil Sakat |
|---|---|
| Primary category | math.OC |
| Published | 7 April 2026 |
| Last updated at source | 7 April 2026 |
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