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In this article, we consider the Tikhonov regularization of an optimal control problem of semilinear partial differential equations with box constraints on the control. We derive a-priori regularization error estimates for the control under…
This paper analyzes a discretization of a stochastic parabolic optimal control problem, where the diffusion term contains the control variable. With rough data, the convergence of the discretization is derived. In addition, a Monte-Carlo…
We propose in this paper a multilevel correction method to solve optimal control problems constrained by elliptic equations with the finite element method. In this scheme, solving optimization problem on the finest finite element space is…
This paper investigates numerical methods for solving stochastic linear quadratic (SLQ) optimal control problems governed by stochastic partial differential equations (SPDEs). Two distinct approaches, the open-loop and closed-loop ones, are…
In this paper, we discuss the numerical approximation of a distributed optimal control problem governed by the von Karman equations, defined in polygonal domains with point-wise control constraints. Conforming finite elements are employed…
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 the finite element discretization and the iterative solution of singularly perturbed elliptic reaction-diffusion equations in three-dimensional computational domains. These equations arise from the optimality conditions for…
This paper deals with the existence of solutions for an elliptic system of partial differential equations. The solution method is based on the sub- and super-solutions approach. An application to a stochastic control problem is presented.…
We present a new parallel computational framework for the efficient solution of a class of $L^2$/$L^1$-regularized optimal control problems governed by semi-linear elliptic partial differential equations (PDEs). The main difficulty in…
An optimal control problem driven by an ordinary differential equation under continuous state constraints is considered in this study. From an operational point of view, we introduce a discrete state constraints optimal control problem and…
The aim of this paper is to extend the global error estimation and control addressed in Lang and Verwer [SIAM J. Sci. Comput. 29, 2007] for initial value problems to finite difference solutions of semilinear parabolic partial differential…
This manuscript presents a framework for using multilevel quadrature formulae to compute the solution of optimal control problems constrained by random partial differential equations. Our approach consists in solving a sequence of optimal…
We are interested in a class of numerical schemes for the optimization of nonlinear hyperbolic partial differential equations. We present continuous and discretized relaxation schemes for scalar, one-- conservation laws. We present…
In this paper, we derive explicit second-order necessary and sufficient optimality conditions of a local minimizer to an optimal control problem for a quasilinear second-order partial differential equation with a piecewise smooth but not…
In this paper, we investigate optimal control problems governed by the parabolic interface equation, in which the control acts on the interface. The solution to this problem exhibits low global regularity due to the jump of the coefficient…
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…
We propose a semi-discrete numerical scheme and establish well-posedness of a class of parabolic systems. Such systems naturally arise while studying the optimal control of grain boundary motions. The latter is typically described using a…
A space-discretization for the elastic flow of inextensible curves is devised and quasi-optimal convergence of the corresponding semi-discrete problem is proved for a suitable discretization of the nonlinear inextensibility constraint.…
The scope of this paper is the analysis and approximation of an optimal control problem related to the Allen-Cahn equation. A tracking functional is minimized subject to the Allen-Cahn equation using distributed controls that satisfy…
We study an optimal control problem under uncertainty, where the target function is the solution of an elliptic partial differential equation with random coefficients, steered by a control function. The robust formulation of the…