Related papers: Fractional semilinear optimal control: optimality …
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…
This work deals with optimal control problems as a strategy to drive bifurcating solution of nonlinear parametrized partial differential equations towards a desired branch. Indeed, for these governing equations, multiple solution…
We derive a-priori error estimates for the finite-element approximation of a distributed optimal control problem governed by the steady one-dimensional Burgers equation with pointwise box constraints on the control. Here the approximation…
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 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 derive error estimates for a linear-quadratic elliptic distributed optimal control problem with pointwise control constraints that can be applied to standard finite element methods and multiscale finite element methods.
This paper continues the investigations from [7] and is concerned with the derivation of first-order conditions for a control constrained optimization problem governed by a non-smooth elliptic PDE. The control enters the state equation not…
This paper explores a fully discrete approximation for a nonlinear hyperbolic PDE-constrained optimization problem (P) with applications in acoustic full waveform inversion. The optimization problem is primarily complicated by the…
We study iterative finite element approximations for the numerical approximation of semilinear elliptic boundary value problems with monotone nonlinear reactions of subcritical growth. The focus of our contribution is on an optimal a priori…
A finite element analysis of a Dirichlet boundary control problem governed by the linear parabolic equation is presented in this article. The Dirichlet control is considered in a closed and convex subset of the energy space $H^1(\Omega…
The aim of this work is to give a broad panorama of the control properties of fractional diffusive models from a numerical analysis and simulation perspective. We do this by surveying several research results we obtained in the last years,…
We consider the optimal control of singular nonlinear partial differential equation which is the distributional formulation of the multiphase Stefan type free boundary problem for the general second order parabolic equation. Boundary heat…
We propose, analyze, and test new iterative solvers for large-scale systems of linear algebraic equations arising from the finite element discretization of reduced optimality systems defining the finite element approximations to the…
We consider fully discrete finite element approximations for a semilinear optimal control system of partial differential equations in two cases: for distributed and Robin boundary control. The ecological predator-prey optimal control model…
In this article, we develop a posteriori error analysis of a nonconforming finite element method for a linear quadratic elliptic distributed optimal control problem with two different set of constraints, namely (i) integral state constraint…
This paper surveys recent analytical and numerical research on linear problems for the integral fractional Laplacian, fractional obstacle problems, and fractional minimal graphs. The emphasis is on the interplay between regularity,…
We consider constrained bilinear optimal control of second-order linear evolution partial differential equations (PDEs) with a reaction term on the half line, where control arises as a time-dependent reaction coefficient and constraints are…
We derive a framework to compute optimal controls for problems with states in the space of probability measures. Since many optimal control problems constrained by a system of ordinary differential equations (ODE) modelling interacting…
In this work, we consider optimal control problems for mechanical systems on vector spaces with fixed initial and free final state and a quadratic Lagrange term. Specifically, the dynamics is described by a second order ODE containing an…
Finite element approximations of Dirichlet boundary control problems governed by parabolic PDEs on convex polygonal domains are studied in this paper. The existence of a unique solution to optimal control problems is guaranteed based on…