PreprintCC BY-NC-SA 4.0arXiv
Simplifying the computation of weak-⋆ second subderivatives of convex functionals via Γ-convergence
Abstract
We prove (under some mild assumptions) that the strong-strong twice epidifferentiability of a convex functional is equivalent to the weak-⋆ twice epidifferentiability of its conjugate functional. Further, the corresponding subderivatives are (up to scaling) conjugates of each other. This result can be used to facilitate the computation of weak-⋆ second subderivatives, which are crucial ingredients in no-gap second-order optimality conditions. We also show that weak-⋆ second subderivatives are invariant under suitable changes of the underlying function space setting.
Related
- Full-Range Γ-Convergence of Weak-Type Nonlocal Functionals
- Fast computation and convergence analysis of the infinite-product representation of the Schottky--Klein prime function
- Accelerated Convergence of a Second-Order Dynamical System and its Application to Splitting Algorithms for Comonotone Inclusions
- Stochastic Augmented Lagrangian Framework with Second-Order Convergence Guarantees for Nonconvex Expectation-Constrained Optimization
- Structural conditions on trust-region radius updates. Part II: second-order convergence and asymptotic radius behaviour
BibTeX
@misc{wachsmuth2026simplifying,
title = {{Simplifying the computation of weak-$\star$ second subderivatives of convex functionals via $Γ$-convergence}},
author = {Gerd Wachsmuth},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.01673},
eprint = {2610.01673},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.01673},
note = {CC BY-NC-SA 4.0},
}
RIS
TY - UNPB
TI - Simplifying the computation of weak-⋆ second subderivatives of convex functionals via Γ-convergence
AU - Gerd Wachsmuth
PY - 2026
DA - 2026/10/01
PB - arXiv
DO - 10.48550/arxiv.2610.01673
UR - https://arxiv.org/abs/2610.01673
AB - We prove (under some mild assumptions) that the strong-strong twice epidifferentiability of a convex functional is equivalent to the weak-⋆ twice epidifferentiability of its conjugate functional. Further, the corresponding subderivatives are (up to scaling) conjugates of each other. This result can be used to facilitate the computation of weak-⋆ second subderivatives, which are crucial ingredients in no-gap second-order optimality conditions. We also show that weak-⋆ second subderivatives are invariant under suitable changes of the underlying function space setting.
ER -