Course content

Examples of optimal control problems for partial differential equations (PDEs). Existence of optimal controls. Control-to-state operators and adjoint states. First and second order optimality conditions. Control of linear and semi-linear elliptic PDEs. Auxiliary results from functional analysis (adjoint operators, differentiability in Banach spaces) and PDEs (weak solutions, Sobolev spaces, calculus of variations). Fundamental numerical methods.

Learning outcome

After meeting the learning objectives of the course, the student will be able to:

1. analyze control-to-state operators for model control problems;
2. derive necessary and sufficient optimality conditions for optimal control problems with or without state constraints;
3. assess existence of solutions to model optimal control problems;
4. implement optimization algorithms on a computer;
5. apply optimization algorithms to model problems.

Learning methods and activities

Lectures, exercises, and project.

Compulsory assignments

• Project

Recommended previous knowledge

The courses TMA4145 Linear Methods and TMA4180 Optimization1 or equivalent. The courses TMA4225 Foundations of Analysis and TMA4220 Numerical Solution of Partial Differential Equations Using Element Methods (or equivalent) are an advantage.

Course materials

Will be announced at the start of the course.