When simulating a mechanism from science or engineering, or an industrial process, one is
frequently required to construct a mathematical model, and then resolve this model …

In this article, we motivate, derive, and test effective preconditioners to be used with the
Minres algorithm for solving a number of saddle point systems which arise in PDE …

Saddle point matrices of a special structure arise in optimal control problems. In this paper
we consider distributed optimal control for various types of scalar stationary partial …

Our times can be characterized by, among many other attributes, the seemingly increasing
speed of everything. Within science, it has led to the publication explosion, which reflects the …

The solution of time-dependent PDE-constrained optimization problems is a challenging
task in numerical analysis and applied mathematics. All-at-once discretizations and …

The solution of Cahn--Hilliard variational inequalities is of interest in many applications. We
discuss the use of them as a tool for binary image inpainting. This has been done before …

Optimal control problems with partial differential equations as constraints play an important
role in many applications. The inclusion of bound constraints for the state variable poses a …

Fractional differential equations have recently received much attention within computational
mathematics and applied science, and their numerical treatment is an important research …

Interior point methods provide an attractive class of approaches for solving linear, quadratic
and nonlinear programming problems, due to their excellent efficiency and wide …

We address the problem of preconditioning a sequence of saddle point linear systems
arising in the solution of PDE-constrained optimal control problems via active-set Newton …