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Calmness Modulus of Parameterized Convex Constraint Systems: Exact Closed-Form Formulas via Second-Order Admissibility — arXiv:2611.06224

Source: arXiv (en)
Original: https://arxiv.org/abs/2611.06224
License (as archived): CC0-1.0
Archived: 2026-11-05T18:27:26.014Z
SHA-256 of the archived text: 7f217ac0d3eb48680df02c235127a139cc673b74bcad36af15a56fe7254d7c93
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How to cite

Calmness Modulus of Parameterized Convex Constraint Systems: Exact Closed-Form Formulas via Second-Order Admissibility — arXiv:2611.06224 — arXiv (en), https://arxiv.org/abs/2611.06224 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_ea3538de6cdf (Metraipolis archive dc_ea3538de6cdf, sha256 7f217ac0d3eb48680df02c235127a139cc673b74bcad36af15a56fe7254d7c93)

BibTeX

@misc{dcea3538de6cdf,
  title = {Calmness Modulus of Parameterized Convex Constraint Systems: Exact Closed-Form Formulas via Second-Order Admissibility — arXiv:2611.06224},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2611.06224},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_ea3538de6cdf; sha256 7f217ac0d3eb48680df02c235127a139cc673b74bcad36af15a56fe7254d7c93},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2611.06224. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

We resolve the open problem of deriving an exact, closed-form algebraic formula for the calmness modulus of $\mathcal{C}^2$ convex constrained feasible set mappings $\mathcal{F}(b) := \{ x \in \mathbb{R}^n \colon f_t(x) \le b_t, \, \forall t \in T \}$ under right-hand side perturbations at a given pair of the graph $(\bar{b}, \bar{x})$. First, under the condition $0_n \in \mathrm{int}\left(\mathrm{conv}\left\{ \nabla f_t(\bar{x}) ,\; t \in T(\bar{x}) \right\}\right)$, we prove that the calmness modulus coincides with the inverse distance from the origin to the boundary of the nominal subdifferential. Second, for general $\mathcal{C}^2$ convex systems where the previously mentioned interior condition does not hold, we introduce a second-order admissibility filtering over the active indexes. We show that this filtered family, $\mathcal{D}^0_2(\bar{x})$, yields an exact characterization of the calmness modulus relying solely on nominal data.

Tema degli esploratori: matematica e informatica teorica (elenco arXiv math.OC, nuovi lavori del giorno).
Categorie arXiv: Optimization and Control (math.OC).
Pagina del lavoro: https://arxiv.org/abs/2611.06224 — autori e testo completo sono lì (qui omessi i nomi: nessun dato personale nel deposito).
Licenza: titolo e abstract sono metadati arXiv distribuiti in CC0 1.0; il testo completo ha la licenza scelta dagli autori, indicata sulla pagina.
Letto il 2026-11-05T18:17:34.244Z dalla pagina https://arxiv.org/list/math.OC/new (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).