Course Contents
Optimization problems are a central topic for almost any working engineer. Examples
include dimensioning of components, minimizing the elastic energy within finite
element methods of modern AI (artificial intelligence) methods. This course introduces
the participants to the basics of nonlinear optimization of differentiable functions.
Furthermore, an overview of different classes of optimization algorithms presented,
discussing which method to apply to a specific problem. In the associated exercise
sessions, solution methods discussed in the lectures will be implemented, also
discussing how to use freely available optimization packages in Python.
Syllabus
• Necessary and sufficient optimizality conditions for unconstrained optimization
• Gradient methods
• Fast and conjugate gradient methods
• Newton and Quasi-Newton methods
• Optimality conditions for constrained optimization
• Projection methods for simple constraints
• Lagrange duality, penalty methods and the method of multipliers
• Interior point methods
• Active set strategies
• Alternating Direction Method of Multipliers (ADMM)
see also https://www.uni-due.de/ingmath/courses.php |
