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arXiv · 2604.05678

Intrinsic perturbation scale for certified oracle objectives with epigraphic information

Karim Bounja·Boujemaâ Achchab·Abdeljalil Sakat
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Abstract

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.

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Karim Bounja, Boujemaâ Achchab, Abdeljalil Sakat. 2026-04-07. Intrinsic perturbation scale for certified oracle objectives with epigraphic information. https://arxiv.org/abs/2604.05678

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