Author

Keegan L. A. Kirk

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Preprint Sep 2026

A Function-Space Framework for BDDC Preconditioning in Control- and State-Constrained Sparse Optimal Control

We develop a Balancing Domain Decomposition by Constraints (BDDC) preconditioner for the interface systems arising from active-set semi-smooth Newton linearizations of elliptic optimal control problems with box-constrained controls, $L^1$-sparsity, and Moreau--Yosida regularized state constraints. The domain decomposit...

H. Antil, Keegan L. A. Kirk, Umarkhon Rakhimov · 0 citations

Preprint Aug 2026

Duality-Based $\textit{A Posteriori}$ Error Identities for Subgradient Flows Based on the Br\'ezis-Ekeland-Nayroles Principle

We derive duality-based $\textit{a posteriori}$ error identities for a broad class of subgradient flows induced by time-dependent convex integral functionals. Starting from the Br\'ezis-Ekeland-Nayroles principle, we identify an unsteady primal energy functional and derive its Fenchel dual formulation, including strong...

H. Antil, Alex Kaltenbach, Keegan L. A. Kirk · 0 citations