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Although originally designed and analyzed for convex problems, the alternating direction method of multipliers (ADMM) and its close relatives, Douglas-Rachford splitting (DRS) and Peaceman-Rachford splitting (PRS), have been observed to…
The Alternating Direction Method of Multipliers (ADMM) provides a natural way of solving inverse problems with multiple partial differential equations (PDE) forward models and nonsmooth regularization. ADMM allows splitting these…
We explore the approximation of feedback control of integro-differential equations containing a fractional Laplacian term. To obtain feedback control for the state variable of this nonlocal equation we use the Hamilton--Jacobi--Bellman…
The aim of this paper is to propose an efficient adaptive finite element method for eigenvalue problems based on the multilevel correction scheme and inverse power method. This method involves solving associated boundary value problems on…
The harmonic balance method is the most commonly used method for solving periodic solutions of nonlinear dynamic systems, but the high-order approximation of nonlinear terms requires sophisticated formula derivation, which limits its…
In this work, we bridge standard adaptive mesh refinement and coarsening on scalable octree background meshes and robust unfitted finite element formulations for the automatic and efficient solution of large-scale nonlinear solid mechanics…
Alternating Direction Method of Multipliers (ADMM) algorithm has been widely adopted for solving the distributed optimization problem (DOP). In this paper, a new distributed parallel ADMM algorithm is proposed, which allows the agents to…
Using the gradient discretisation method (GDM), we provide a complete and unified numerical analysis for non-linear variational inequalities (VIs) based on Leray--Lions operators and subject to non-homogeneous Dirichlet and Signorini…
This paper studies efficient distributed optimization methods for multi-agent networks. Specifically, we consider a convex optimization problem with a globally coupled linear equality constraint and local polyhedra constraints, and develop…
In this paper, we aim to provide a comprehensive analysis on the linear rate convergence of the alternating direction method of multipliers (ADMM) for solving linearly constrained convex composite optimization problems. Under a certain…
We propose a scalable method for computing global solutions of nonlinear, high-dimensional dynamic stochastic economic models. First, within a time iteration framework, we approximate economic policy functions using an adaptive,…
Linearized alternating direction method of multipliers (ADMM) as an extension of ADMM has been widely used to solve linearly constrained problems in signal processing, machine leaning, communications, and many other fields. Despite its…
We introduce a distributed adaptive quadrature method that formulates multidimensional integration as a hierarchical domain decomposition problem on multi-GPU architectures. The integration domain is recursively partitioned into subdomains…
This article reports an algorithm for multi-agent distributed optimization problems with a common decision variable, local linear equality and inequality constraints and set constraints with convergence rate guarantees.…
This paper presents a hybrid numerical method to solve efficiently a class of highly anisotropic elliptic problems. The anisotropy is aligned with one coordinate-axis and its strength is described by a parameter $\eps \in (0,1]$, which can…
In this paper, we present a fast and accurate numerical scheme for the solution of fifth-order boundary-value problems. We apply the reproducing kernel Hilbert space method (RKHSM) for solving this problem. The analytic results of the…
Multi-frequency, highly-oscillatory Hamiltonian problems derive from the mathematical modelling of many real life applications. We here propose a variant of Hamiltonian Boundary Value Methods (HBVMs), which is able to efficiently deal with…
The estimation of multiple parameters in quantum metrology is important for a vast array of applications in quantum information processing. However, the unattainability of fundamental precision bounds for incompatible observables has…
Despite the extensive application of nonlinear Model Predictive Control (MPC) in automated driving, balancing its computational efficiency with respect to the control performance and constraint satisfaction remains a challenge in emergency…
We present an approximate method for solving nonlinear control problems over long time horizons, in which the full nonlinear model is preserved over an initial part of the horizon, while the remainder of the horizon is modeled using a…