Related papers: New time domain decomposition methods for paraboli…
In this paper, we consider a primal-dual domain decomposition method for total variation regularized problems appearing in mathematical image processing. The model problem is transformed into an equivalent constrained minimization problem…
We consider optimal control problems for partial differential equations where the controls take binary values but vary over the time horizon, they can thus be seen as dynamic switches. The switching patterns may be subject to combinatorial…
We develop innovative algorithms for solving the strong-constraint formulation of four-dimensional variational data assimilation in large-scale applications. We present a space-time decomposition approach that employs domain decomposition…
We introduce a new domain decomposition strategy for time harmonic Maxwell's equations that is valid in the case of automatically generated subdomain partitions with possible presence of cross-points. The convergence of the algorithm is…
We study Benamou's domain decomposition algorithm for optimal transport in the entropy regularized setting. The key observation is that the regularized variant converges to the globally optimal solution under very mild assumptions. We prove…
In this paper we study the conditioning of optimal control problems constrained by linear parabolic equations with Neumann boundary conditions. While we concentrate on a given end-time target function the results hold also when the target…
A new algorithm for solving large-scale convex optimization problems with a separable objective function is proposed. The basic idea is to combine three techniques: Lagrangian dual decomposition, excessive gap and smoothing. The main…
We are interested in high-order linear multistep schemes for time discretization of adjoint equations arising within optimal control problems. First we consider optimal control problems for ordinary differential equations and show loss of…
The time parallel solution of optimality systems arising in PDE constraint optimization could be achieved by simply applying any time parallel algorithm, such as Parareal, to solve the forward and backward evolution problems arising in the…
Neural networks (NNs) have gained significant attention across various engineering disciplines, particularly in design optimization, where they are used to build surrogate models for high-dimensional regression problems. Despite their power…
We present a temporal decomposition scheme for solving long-horizon optimal control problems. In the proposed scheme, the time domain is decomposed into a set of subdomains with partially overlapping regions. Subproblems associated with the…
We develop two new variants of alternating direction methods of multipliers (ADMM) and two parallel primal-dual decomposition algorithms to solve a wide range class of constrained convex optimization problems. Our approach relies on a novel…
In this work, we address parametric non-stationary fluid dynamics problems within a model order reduction setting based on domain decomposition. Starting from the optimisation-based domain decomposition approach, we derive an optimal…
We present a Waveform Relaxation (WR) version of the Dirichlet-Neumann and Neumann-Neumann algorithms for the wave equation in space time. Each method is based on a non-overlapping spatial domain decomposition, and the iteration involves…
Receding horizon optimal control problems compute the solution at each time step to operate the system on a near-optimal path. However, in many practical cases, the boundary conditions, such as external inputs, constraint equations, or the…
In this paper, we investigate optimal control problems governed by semilinear elliptic variational inequalities involving constraints on the state, and more precisely the obstacle problem. Since we adopt a numerical point of view, we first…
We propose a time domain decomposition approach to optimal control of partial differential equations (PDEs) based on semigroup theoretic methods. We formulate the optimality system consisting of two coupled forward-backward PDEs, the state…
In this contribution we propose reduced order methods to fast and reliably solve parametrized optimal control problems governed by time dependent nonlinear partial differential equations. Our goal is to provide a tool to deal with the time…
Domain decomposition (DD) methods for solving time-dependent problems can be classified by (i) the method of domain decomposition used, (ii) the choice of decomposition operators (exchange of boundary conditions), and (iii) the splitting…
In this article, we have studied the convergence behavior of the Dirichlet-Neumann and Neumann- Neumann waveform relaxation algorithms for time-fractional sub-diffusion and diffusion-wave equations in 1D & 2D for regular domains, where the…