相关论文: Multigrid solution of a distributed optimal contro…

A finite horizon linear quadratic(LQ) optimal control problem is studied for a class of discrete-time linear fractional systems (LFSs) affected by multiplicative, independent random perturbations. Based on the dynamic programming technique,…

In this paper we study fast iterative solvers for the large sparse linear systems resulting from the stochastic Galerkin discretization of stochastic partial differential equations. A block triangular preconditioner is introduced and…

We present an optimal preconditioner for the exactly divergence-free discontinuous Galerkin (DG) discretization of Cockburn, Kanschat, and Sch\"otzau [J. Sci. Comput., 31 (2007), pp. 61--73] and Wang and Ye [SIAM J. Numer. Anal., 45 (2007),…

This work deals with the existence of optimal solution and the maximum principle for optimal control problem governed by Navier-Stokes equations with state constraint in 3-D. Strong results in 2-D also are given.

The coupled Darcy-Stokes problem is widely used for modeling fluid transport in physical systems consisting of a porous part and a free part. In this work we consider preconditioners for monolitic solution algorithms of the coupled…

Numerical simulation of incompressible fluid flows has been an active topic of research in Scientific Computing for many years, with many contributions to both discretizations and linear and nonlinear solvers. In this work, we propose an…

We present a first step towards a multigrid method for solving the min-cost flow problem. Specifically, we present a strategy that takes advantage of existing black-box fast iterative linear solvers, i.e. algebraic multigrid methods. We…

In this paper we discuss optimality conditions for abstract optimization problems over complex spaces. We then apply these results to optimal control problems with a semigroup structure. As an application we detail the case when the state…

Due to its optimal complexity, the multigrid (MG) method is one of the most popular approaches for solving large-scale linear systems arising from the discretization of partial differential equations. However, the parallel implementation of…

We consider the time-dependent Stokes-Darcy problem as a model case for the challenges involved in solving coupled systems. Keeping the model, its discretization, and the underlying numerics for the subproblems in the free-flow domain and…

The aim of this paper is to design an efficient multigrid method for constrained convex optimization problems arising from discretization of some underlying infinite dimensional problems. Due to problem dependency of this approach, we only…

In this paper we address the problem of information-constrained optimal control for an interconnected system subject to one-step communication delays and power constraints. The goal is to minimize a finite-horizon quadratic cost by…

In this paper, we propose a centralized secondary control for the real-time steady-state optimization of multi-terminal HVdc grids under voltage and current limits. First, we present the dynamic models of the grid components, including the…

Stochastic Model Predictive Control has proved to be an efficient method to plan trajectories in uncertain environments, e.g., for autonomous vehicles. Chance constraints ensure that the probability of collision is bounded by a predefined…

In this paper, we consider the problem of multi-objective optimal control of a dynamical system with additive and multiplicative noises with given second moments and arbitrary probability distributions. The objectives are given by quadratic…

We study a stochastic optimal control problem for fully coupled forward-backward stochastic control systems with a nonempty control domain. For our problem, the first-order and second-order variational equations are fully coupled linear…

We propose a partitioned method for the monolithic formulation of the Stokes-Biot system that incorporates Lagrange multipliers enforcing the interface conditions. The monolithic system is discretized using finite elements, and we establish…

This work introduces and assesses the efficiency of a monolithic $ph$MG multigrid framework designed for high-order discretizations of stationary Stokes systems using Taylor-Hood and Scott-Vogelius elements. The proposed approach integrates…

We consider the application of the Douglas-Rachford (DR) algorithm to solve linear-quadratic (LQ) control problems with box constraints on the state and control variables. We split the constraints of the optimal control problem into two…

The solution of saddle-point problems, such as the Stokes equations, is a challenging task, especially in large-scale problems. Multigrid methods are one of the most efficient solvers for such systems of equations and can achieve…