Work

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

Year: 2026

Type: preprint

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.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2610.01673

Author: Wachsmuth, Gerd

Institution: Brandenburg University of Technology Cottbus-Senftenberg

Language: English

Topic: Optimization and Variational Analysis

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: green

Funders: Deutsche Forschungsgemeinschaft, Universität Wien

Award: G5188812543

OpenAlex ID: W7215868500

Cites: 22

Cited by:

Related to: 10