相关论文: An FE-dABCD algorithm for elliptic optimal control…
We propose and analyze a new discretization technique for a linear-quadratic optimal control problem involving the fractional powers of a symmetric and uniformly elliptic second oder operator; control constraints are considered. Since these…
This article is concerned with the nonconforming finite element method for distributed elliptic optimal control problems with pointwise constraints on the control and gradient of the state variable. We reduce the minimization problem into a…
We consider a class of parameter-dependent optimal control problems of elliptic PDEs with constraints of general type on the control variable. Applying the concept of variational discretization, [4], together with techniques from the…
We study an optimal control problem governed by elliptic PDEs with interface, which the control acts on the interface. Due to the jump of the coefficient across the interface and the control acting on the interface, the regularity of…
In this paper we consider the convergence analysis of adaptive finite element method for elliptic optimal control problems with pointwise control constraints. We use variational discretization concept to discretize the control variable and…
Optimization problems with $L^1$-control cost functional subject to an elliptic partial differential equation (PDE) are considered. However, different from the finite dimensional $l^1$-regularization optimization, the resulting discretized…
We study the numerical approximation of linear-quadratic optimal control problems subject to the fractional Laplace equation with its spectral definition. We compute an approximation of the state equation using a discretization of the…
In this paper, we investigate optimal control problems governed by semilinear elliptic variational inequalities involving constraints on the state, and more precisely the obstacle problem. Since we adopt a numerical point of view, we first…
In this paper we discuss the numerical solution of elliptic distributed optimal control problems with state or control constraints when the control is considered in the energy norm. As in the unconstrained case we can relate the…
We adopt the integral definition of the fractional Laplace operator and analyze solution techniques for fractional, semilinear, and elliptic optimal control problems posed on Lipschitz polytopes. We consider two strategies of…
The study of optimal control problems under uncertainty plays an important role in scientific numerical simulations. This class of optimization problems is strongly utilized in engineering, biology and finance. In this paper, a stochastic…
We consider discontinuous Galerkin methods for an elliptic distributed optimal control problem constrained by a convection-dominated problem. We prove global optimal convergence rates using an inf-sup condition, with the diffusion parameter…
We consider an abstract framework for the numerical solution of optimal control problems (OCPs) subject to partial differential equations (PDEs). Examples include not only the distributed control of elliptic PDEs such as the Poisson…
In this paper we propose a new finite element method for solving elliptic optimal control problems with pointwise state constraints, including the distributed controls and the Dirichlet or Neumann boundary controls. The main idea is to use…
We consider an elliptic optimal control problem where the objective functional contains evaluations of the state at a finite number of points. In particular, we use a fidelity term that encourages the state to take certain values at these…
In this paper we investigate a priori error estimates for the space-time Galerkin finite element discretization of an optimal control problem governed by a simplified linear gradient enhanced damage model. The model equations are of a…
Recently the authors have studied a state and control constrained optimal control problem with fractional elliptic PDE as constraints. The goal of this paper is to continue that program forward and introduce an algorithm to solve such…
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…
We consider a linear-quadratic optimization problem with pointwise bounds on the state for which the constraint is given by the Laplace-Beltrami equation (to have uniqueness we add an lower order term) on a two-dimensional surface . By…
This paper focusses on the optimal control problems governed by fourth-order linear elliptic equations with clamped boundary conditions in the framework of the Hessian discretisation method (HDM). The HDM is an abstract framework that…