Mathematics and numerics in PDE-constrained optimization problems with state and control constraints

Project highlights:

Optimal design, optimal control and parameter estimation of systems governed by partial differential equations (PDE) give rise to a class of problems referred to as PDE-constrained optimization (OPT-PDE). OPT-PDE pursues the idea to influence phenomena and processes, governed by PDEs. As PDEs describe almost every aspect of physics, chemistry, engineering, biology, finance etc., that fit into a continuum framework, OPT-PDE can be regarded as the ultimate/farthermost goal of any application problem to steer the underlying systems in a desired way.

As a starting point, we consider the OPT-PDE setting with a stationary or time-dependent reaction-diffusion equation as constraint, combined with pointwise (box) constraints of the state and the control variable, which latter is in addition sparse (localized).

The aim of the project is two-fold. On the modelling and discretization side we will

On the solution method side we will

First results:

   State         Control        State        Control    
State Control State Sparse control

Article in review: I. Dravins, M. Neytcheva, PDE-Constrained Optimization: Matrix Structures and Preconditioners

As a far goal, the constraint could be extended to a system of equations, to model coupled heating-cooling physics processes.
Maya Neytcheva     Gunilla Kreiss     Ivo Dravins
Scientific Computing, Uppsala University

Last changed on March 11, 2017
Mail to: Maya dot Neytcheva "at" it dot uu dot se "