Teaching

The WG Numerical Optimization provides the following lectures in the field of optimization:

Optimization I (Unrestricted Nonlinear Optimization):

The course consists of a two-hour lecture and a one-hour tutorial and is offered every summer semester. The course provides an introduction to the research field of numerical optimization. Unconstrained optimization problems are considered and different numerical solution methods are introduced. An outline of the lecture is as follows:

  1. Introduction
  2. Optimality Conditions
  3. Convexity and Convex Optimization
  4. Descent Methods and Step Size Strategies – Part 1
  5. Descent Methods and Step Size Strategies – Part 2
  6. Descent Methods and Step Size Strategies – Part 3
  7. Steepest descent and conjugate gradient methods - Part 1
  8. Steepest descent and conjugate gradient methods - Part 2
  9. Rates of Convergence
  10. Newton’s Method - Part 1
  11. Newton’s Method - Part 2
  12. Quasi-Newton Methods

Prerequisites for the course: Analysis I and II, Linear Algebra, Numerics I, PYTHON programming knowledge.

Creditability:
- Bachelor Mathematics: Supplementary module
- Bachelor Mathematical Finance: Module Numerics and Optimization
- Master of Education Mathematics: Elective module and oral final examination

Optimization II (Restricted Nonlinear Optimization):

This course is a four-hour lecture and a two-hour tutorial. The course is offered in the winter term and focuses on constrained nonlinear optimization. An outline of the lecture is as follows:

  1. Optimality Conditions for Constrained Optimization - Part 1
  2. Optimality Conditions for Constrained Optimization - Part 2
  3. Introduction to Linear Programming
  4. Interior-Point Methods for Linear Programming – Part 1
  5. Interior-Point Methods for Linear Programming – Part 2
  6. Quadratic Programming – Part 1
  7. Quadratic Programming – Part 2
  8. Penalty Methods
  9. Augmented Lagrangian Method
  10. Nonlinear Problems with Box Constraints – Part 1
  11. Nonlinear Problems with Box Constraints – Part 2
  12. Sequential Quadratic Programming – Part 1
  13. Sequential Quadratic Programming – Part 2

The lecture is divided into two parts, of which in particular only the first part (4.5 ECTS) can be attended separately.

Prerequisites for the course: Analysis I and II, Linear Algebra, Numerics I, Optimization I, PYTHON programming skills.

Creditability:
- Master Mathematics: Main and elective module
- Master Mathematical Finance: Elective module
- Master of Education Mathematics: Elective module and oral final exam (e.g. the first part of Optimization II together with Optimization I)

Optimization III (Further Topics on Optimization):

This course consists of a two-hour lecture and a one-hour tutorial and is usually offered in the summer term. The goal is to give an introduction to further topics in nonlinear optimization which are studied in detail in continuing lectures (Optimization IV). The covered topics are as follows:
- Finite Dimensional Optimal Control Problems
- Multiobjective Optimization
- Model Reduction using Proper Orthogonal Decomposition
- Linear-Quadratic Optimal Control
- Stochastic gradient descent

Prerequisites for the course: Analysis I and II, Linear Algebra, Numerics I, Optimization I, Optimization II (desirable).

Creditability:
- Master Mathematics: Specialization module
- Master Financial Mathematics: Elective module

Optimization IV:

For further specialization in numerical optimization, lectures from the following list are offered on a regular basis (in addition to specialized seminars):

- Optimization of Elliptic Differential Equations (2 h Lecture, 1 h Tutorial, 5 ECTS)
- Optimal Control of Differential Equations (2 h Lecture, 1 h Tutorial, 5 ECTS)
- Proper Orthogonal Decomposition for Linear-Quadratic Optimal Control (2 h Lecture, 1 h Tutorial, 5 ECTS)

Creditability:
- Master Mathematics: Specialization module
- Master Mathematical Finance: Elective module

Previous lectures

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