The aim of this seminar is to discuss numerical methods for optimization problems.

Many problems in science, engineering or finance can be formulated as optimization problems.

Mathematically, an optimization problem seeks a minimizer x of a "cost function" f(x). Hereby, one distinguishes unconstrained problems, where a solution in R^d is sought, and constraint problems, where x has to satisfy additional equations or inequalities

In this seminar, we will deal with numerical methods for optimization problems. For example, the following topics will be discussed:

• Unconstrained optimization: Line-search-methods, trust-region-methods
• Constrained optimization: linear programming, Simplex-algorithm, penalty-methods
• Nonlinear optimization: quadratic programming, interior-point-methods, gradient-projection-methods
• Optimal control
• Non-smooth optimization