Related papers: Multigrid methods for saddle point problems: Karus…
We present necessary and sufficient optimality conditions for finite time optimal control problems for a class of hybrid systems described by linear complementarity models. Although these optimal control problems are difficult in general…
The present work develops hybrid multigrid methods for high-order discontinuous Galerkin discretizations of elliptic problems. Fast matrix-free operator evaluation on tensor product elements is used to devise a computationally efficient PDE…
In this work we construct multigrid preconditioners to accelerate the solution process of a linear-quadratic optimal control problem constrained by the Stokes system. The first order optimality conditions of the control problem form a…
A fast multigrid solver is presented for high-order accurate Stokes problems discretised by local discontinuous Galerkin (LDG) methods. The multigrid algorithm consists of a simple V-cycle, using an element-wise block Gauss-Seidel smoother.…
We solve large-scale mixed-integer linear programs (MILPs) via distributed asynchronous saddle point computation. This is motivated by the MILPs being able to model problems in multi-agent autonomy, e.g., task assignment problems and…
This paper concerns two algorithms for solving optimal control problems with hybrid systems. The first algorithm aims at hybrid systems exhibiting sliding modes. The first algorithm has several features which distinguishes it from the other…
In this paper we analyse the convergence properties of V-cycle multigrid algorithms for the numerical solution of the linear system of equations arising from discontinuous Galerkin discretization of second-order elliptic partial…
In the past decades, a remarkable amount of research has been carried out regarding fast solvers for large linear systems resulting from various discretizations of fractional differential equations (FDEs). In the current work, we focus on…
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…
To numerically solve a generic elliptic equation on two-dimensional domains with rectangular Cartesian grids, we propose a cut-cell geometric multigrid method that features (1) general algorithmic steps that apply to two-dimensional…
In this note we present a multigrid preconditioning method for solving quadratic optimization problems constrained by a fractional diffusion equation. Multigrid methods within the all-at-once approach to solve the first order-order…
In this paper we analyze the convergence properties of two-level and W-cycle multigrid solvers for the numerical solution of the linear system of equations arising from hp-version symmetric interior penalty discontinuous Galerkin…
We propose a regularized saddle-point algorithm for convex networked optimization problems with resource allocation constraints. Standard distributed gradient methods suffer from slow convergence and require excessive communication when…
This paper considers continuous-time coordination algorithms for networks of agents that seek to collectively solve a general class of nonsmooth convex optimization problems with an inherent distributed structure. Our algorithm design…
Saddle-point or primal-dual methods have recently attracted renewed interest as a systematic technique to design distributed algorithms which solve convex optimization problems. When implemented online for streaming data or as dynamic…
In this work, we develop a collection of novel methods for the entropic-regularised optimal transport problem, which are inspired by existing mirror descent interpretations of the Sinkhorn algorithm used for solving this problem. These are…
We search saddle points for a large class of convex-concave Lagrangian. A generalized explicit iterative scheme based on Arrow-Hurwicz method converges to a saddle point of the problem. We also propose in this work, a convergent…
In this work we recast parametrized time dependent optimal control problems governed by partial differential equations in a saddle point formulation and we propose reduced order methods as an effective strategy to solve them. Indeed, on one…
We construct and analyze a multiscale finite element method for an elliptic distributed optimal control problem with pointwise control constraints, where the state equation has rough coefficients. We show that the performance of the…
We study an optimal distributed control problem associated to a stochastic Cahn-Hilliard equation with a classical double-well potential and Wiener multiplicative noise, where the control is represented by a source-term in the definition of…