Optimization 2

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.

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.

Lectures, exercises, and project.