In this paper a review of the results on sparse controls for partial differential equations is
presented. There are two different approaches to the sparsity study of control problems. One …

This paper investigates stability properties of affine optimal control problems constrained by
semilinear elliptic partial differential equations. This is done by studying the so called metric …

The problem of optimal placement of point sources is formulated as a distributed optimal
control problem with sparsity constraints. For practical relevance, partial observations as …

This paper is dedicated to the stability analysis of the optimal solutions of a control problem
associated with a semilinear elliptic equation. The linear differential operator of the equation …

In this paper, we investigate solution stability for control problems of partial differential
equations with the cost functional not involving the usual quadratic term for the control. We …

This work is concerned with the iterative regularization of a non-smooth nonlinear ill-posed
problem where the forward mapping is merely directionally but not Gâteaux differentiable …

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 …

We study the finite element approximation of an optimal control problem governed by a
semilinear partial differential equation and whose objective function includes a term …

Ill-posed optimization problems appear in a wide range of mathematical applications, and
their numerical solution requires the use of appropriate regularization techniques. In order to …

We consider Tikhonov regularization of control-constrained optimal control problems. We
present new a-priori estimates for the regularization error assuming measure and source …