Related papers: Convergence analysis of inexact two-grid methods: …
Neural networks have become a prominent approach to solve inverse problems in recent years. Amongst the different existing methods, the Deep Image/Inverse Priors (DIPs) technique is an unsupervised approach that optimizes a highly…
This paper investigates a symmetric dual-wind discontinuous Galerkin (DWDG) method for solving an elliptic optimal control problem with control constraints. The governing constraint is an elliptic partial differential equation (PDE), which…
This paper expands the Cyclic Block Proximal Gradient method for block separable composite minimization by allowing for inexactly computed gradients and proximal maps. The resultant algorithm, the Inexact Cyclic Block Proximal Gradient…
This paper presents the integration of constraint propagation and dual proof analysis in an exact, roundoff-error-free MIP solver. The authors employ safe rounding methods to ensure that all results remain provably correct, while…
The goal of this paper is to further develop an approach to inverse problems with imperfect forward operators that is based on partially ordered spaces. Studying the dual problem yields useful insights into the convergence of the…
The heart of the a priori and a posteriori error control in convex minimization problems is the sharp control of the differences of discrete and exact minimal energy. Conforming finite element discretizations for p-Laplace type minimization…
We propose an algorithm for generating explicit solutions of multiparametric mixed-integer convex programs to within a given suboptimality tolerance. The algorithm is applicable to a very general class of optimization problems, but is most…
The speed of sound in two-phase pipe flow systems is often several orders of magnitude greater than the travelling speed of hydraulic information (volume fractions.) Dynamically simulating such flows requires resolution of acoustic and…
I make three conceptual points regarding multigrid methods for computing propagators in lattice gauge theory: 1) The class of operators handled by the algorithm must be stable under coarsening. 2) Problems related by symmetry should have…
In this paper, we propose a $W$-cycle $p$-multigrid method for solving the $p$-version symmetric interior penalty discontinuous Galerkin (SIPDG) discretization of elliptic problems. This SIPDG discretization employs hierarchical Legendre…
The least square solution of minimum norm of a rectangular linear system of equations can be found out iteratively by using matrix splittings. However, the convergence of such an iteration scheme arising out of a matrix splitting is…
Smart grid's objective is to enable electricity and information to flow two-way while providing effective, robust, computerized, and decentralized energy delivery. This necessitates the use of state estimation-based techniques and real-time…
We consider the parallel time integration of the linear advection equation with the Parareal and two-level multigrid-reduction-in-time (MGRIT) algorithms. Our aim is to develop a better understanding of the convergence behaviour of these…
This papers highlights the benefit of coordinating resources on mulitple active distribution feeders during severe long duration outages through multi-microgrid formation. A graph-theory based multi-microgrid formation algorithm is…
The aim of this paper is to develop stable and accurate numerical schemes for boundary integral formulations of the heat equation with Dirichlet boundary conditions. The accuracy of Galerkin discretisations for the resulting boundary…
A wide variety of different (fixed-point) iterative methods for the solution of nonlinear equations exists. In this work we will revisit a unified iteration scheme in Hilbert spaces from our previous work that covers some prominent…
Finite element methods for symmetric linear hyperbolic systems using unstructured advancing fronts (satisfying a causality condition) are considered in this work. Convergence results and error bounds are obtained for mapped tent pitching…
This paper deals with the efficient numerical solution of single-phase flow problems in fractured porous media. A monolithic multigrid method is proposed for solving two-dimensional arbitrary fracture networks with vertical and/or…
In this article, an abstract framework for the error analysis of discontinuous Galerkin methods for control constrained optimal control problems is developed. The analysis establishes the best approximation result from a priori analysis…
Motivated by recent work on stochastic gradient descent methods, we develop two stochastic variants of greedy algorithms for possibly non-convex optimization problems with sparsity constraints. We prove linear convergence in expectation to…