Simplifying the computation of weak-$\star$ second subderivatives of convex functionals via $Γ$-convergence

Gerd Wachsmuth

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arXiv · 2610.01673

Simplifying the computation of weak-$\star$ second subderivatives of convex functionals via $Γ$-convergence

Gerd Wachsmuth

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Abstract

We prove (under some mild assumptions) that the strong-strong twice epidifferentiability of a convex functional is equivalent to the weak-$\star$ 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-$\star$ second subderivatives, which are crucial ingredients in no-gap second-order optimality conditions. We also show that weak-$\star$ second subderivatives are invariant under suitable changes of the underlying function space setting.

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BibTeX RIS

Gerd Wachsmuth. 2026-10-01. Simplifying the computation of weak-$\star$ second subderivatives of convex functionals via $Γ$-convergence. https://arxiv.org/abs/2610.01673

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