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This work proves $O(j^{-1})$ gap bounds for both recovered and averaged primal candidates and gives a sharper bound on the primal error for exactly recovered points, and proves the dual proximal-gradient method produces finite gaps tending to zero.
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...
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...
Abstract We study Maxwell’s equations in conducting media with perfectly conducting boundary conditions on Lipschitz domains, allowing rough material coefficients and L 2-data. Our first contribution is a direct proof of well-posedness (existence, uniqueness and continuous dependence on data) of the first-order weak fo...
We propose a reduced order modeling (ROM) framework for 1D conservative PDEs based on the cumulative distribution transform (CDT). The CDT maps nonnegative, equal-mass states into a Hilbert space in which 1D Wasserstein distances become weighted $L^2$ distances and translations become affine shifts. This makes the tran...
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