Related papers: Multigrid solution of a distributed optimal contro…
This paper investigates the stochastic linear-quadratic control problems with affine constraints, in which both equality and inequality constraints are involved. With the help of the Pontryagin maximum principle and Lagrangian duality…
Coupled systems of free flow and porous media arise in a variety of technical and environmental applications. For laminar flow regimes, such systems are described by the Stokes equations in the free-flow region and Darcy's law in the porous…
An interior point method for the structural topology optimization is proposed. The linear systems arising in the method are solved by the conjugate gradient method preconditioned by geometric multigrid. The resulting method is then compared…
This is a tutorial and survey paper on Karush-Kuhn-Tucker (KKT) conditions, first-order and second-order numerical optimization, and distributed optimization. After a brief review of history of optimization, we start with some preliminaries…
Most research on preconditioners for time-dependent PDEs has focused on implicit multi-step or diagonally-implicit multi-stage temporal discretizations. In this paper, we consider monolithic multigrid preconditioners for fully-implicit…
We propose an efficient iterative method to solve the mixed Stokes-Dracy model for coupling fluid and porous media flow. The weak formulation of this problem leads to a coupled, indefinite, ill-conditioned and symmetric linear system of…
In this paper, we present a multigrid preconditioner for solving the linear system arising from the piecewise linear nonconforming Crouzeix-Raviart discretization of second order elliptic problems with jump coefficients. The preconditioner…
In this paper, preconditioning the saddle point problem arising from the elliptic boundary optimal control problem with mixed boundary conditions is considered. A block triangular reconditioning method is proposed based on permutations of…
The importance of Schur complement based preconditioners are well-established for classical saddle point problems in $\mathbb{R}^N \times \mathbb{R}^M$. In this paper we extend these results to multiple saddle point problems in Hilbert…
In this work, we propose a novel diagonalization-based preconditioner for the all-at-once linear system arising from the optimal control problem of parabolic equations. The proposed preconditioner is constructed based on an…
We propose a preconditioner to accelerate the convergence of the GMRES iterative method for solving the system of linear equations obtained from discretize-then-optimize approach applied to optimal control problems constrained by a partial…
We investigate the discrete-time stochastic linear quadratic control problem for a population of cooperative agents under the hard equality constraint on total control inputs, motivated by demand response in renewable energy systems. We…
We introduce tensor numerical techniques for solving optimal control problems constrained by elliptic operators in $\mathbb{R}^d$, $d=2,3$, with variable coefficients, which can be represented in a low rank separable form. We construct a…
In this paper, we consider a state constrained optimal control problem governed by the transient Stokes equations. The state constraint is given by an L2 functional in space, which is required to fulfill a pointwise bound in time. The…
We analyze a bilinear optimal control problem for the Stokes--Brinkman equations: the control variable enters the state equations as a coefficient. In two- and three-dimensional Lipschitz domains, we perform a complete continuous analysis…
The discretization of robust quadratic optimal control problems under uncertainty using the finite element method and the stochastic collocation method leads to large saddle-point systems, which are fully coupled across the random…
This work focuses on the iterative solution of sequences of KKT linear systems arising in interior point methods applied to large convex quadratic programming problems. This task is the computational core of the interior point procedure and…
This paper presents a matrix-free multigrid method for solving the Stokes problem, discretized using $H^{\text{div}}$-conforming discontinuous Galerkin methods. We employ a Schur complement method combined with the fast diagonalization…
This paper is concerned with the distributed optimal control of a time-discrete Cahn--Hilliard/Navier--Stokes system with variable densities. It focuses on the double-obstacle potential which yields an optimal control problem for a family…
From economics point of view, we investigate a new optimal control problem driven by a stochastic differential equation with a multi-time states cost functional. By constructing a series of first-order adjoint equations, we establish the…