Time and place

Tutorial / flipped classroom: Di, 14-16h, HS II, Albertstr. 23b
Sir-in Exam: Date to be announced

Teacher: Moritz Diehl
Assistant: Léo Simpson
Language: in English

The aim of the course is to give an introduction into numerical methods for the solution of optimization problems in science and engineering. The focus is on continuous nonlinear optimization in finite dimensions, covering both convex and nonconvex problems. The course divided into four major parts:

1. Fundamental Concepts of Optimization: Definitions, Types of Optimization Problems, Convexity, Duality, Compu- ting Derivatives
2. Unconstrained Optimization and Newton-Type Algorithms: Exact Newton, Quasi-Newton, BFGS, Gauss-Newton, Globalization
3. Equality Constrained Optimization: Optimality Conditions, Newton-Lagrange and Constrained Gauss–Newton, Quasi-Newton, Globalization
4. Inequality Constrained Optimization Algorithms: Karush-Kuhn-Tucker Conditions, Active Set Methods, Interior Point Methods, Sequential Quadratic Programming

The course is organized as inverted classroom based on lecture recordings and a lecture manuscript, with weekly alternating Q&A sessions and exercise sessions. The lecture is accompanied by intensive computer exercises offered in Python (6 ECTS) and an optional project (3 ECTS). The project consists in the formulation and implementation of a self-chosen optimization problem or numerical solution method, resulting in documented computer code, a project report, and a public presentation. Please check the website for further information.

necessary: Analysis I–II, Linear Algebra I–II

useful: Introduction to Numerics

Elective (Option Area) (2HfB21)
Compulsory Elective in Mathematics (BSc21)
Supplementary Module in Mathematics (MEd18)
Applied Mathematics (MSc14)
Mathematics (MSc14)
Concentration Module (MSc14)
Elective (MSc14)
Elective in Data (MScData24)

Time and place

Lecture: Di, Do, 8-10h, HS II, Albertstr. 23b
Tutorial: 2 hours, date to be determined
Computer exercise: 2 hours, date to be determined

Teacher: Moritz Diehl, Patrick Dondl, Angelika Rohde
Assistant: Ben Deitmar, Coffi Aristide Hounkpe
Language: in English

This course provides an introduction into the basic concepts, notions, definitions and results in probability theory, numerics and optimization, accompanied with programming projects in Python. Besides deepen mathematical skills in principle, the course lays the foundation of further classes in these three areas.

None that go beyond admission to the degree programme.

Basics in Applied Mathematics (MScData24)

Time and place

Tutorial / flipped classroom: Di, 14-16h, HS II, Albertstr. 23b

Teacher: Moritz Diehl
Assistant: Florian Messerer
Language: in English

The aim of the course is to give an introduction to numerical methods for the solution of optimal control problems in science and engineering. The focus is on both discrete time and continuous time optimal control in continuous state spaces. It is intended for a mixed audience of students from mathematics, engineering and computer science.

The course covers the following topics:

• Introduction to Dynamic Systems and Optimization
• Rehearsal of Newton-type methods and Numerical Optimization
• Algorithmic Differentiation
• Discrete Time Optimal Control
• Dynamic Programming
• Continuous Time Optimal Control
• Numerical Simulation Methods
• Hamilton–Jacobi–Bellmann Equation
• Pontryagin and the Indirect Approach
• Direct Optimal Control
• Real-Time Optimization for Model Predictive Control

The lecture is accompanied by intensive weekly computer exercises offered both in MATLAB and Python (6~ECTS) and an optional project (3~ECTS). The project consists in the formulation and implementation of a self-chosen optimal control problem and numerical solution method, resulting in documented computer code, a project report, and a public presentation.

Required: Analysis~I and II, Linear Algebra~I and II \ Recommended: Numerics I, Ordinary Differential Equations, Numerical Optimization

Elective (Option Area) (2HfB21)
Compulsory Elective in Mathematics (BSc21)
Supplementary Module in Mathematics (MEd18)
Applied Mathematics (MSc14)
Mathematics (MSc14)
Concentration Module (MSc14)
Elective (MSc14)
Elective in Data (MScData24)

Time and place

Lecture: Mo, 8: 30-10h, HS 00-026, Georges-Köhler-Allee 101, Mi, 8: 30-10h, HS 00-036, Georges-Köhler-Allee 101
Tutorial: 2 hours, various dates

Teacher: Moritz Diehl
Language: in English

Elective in Data (MScData24)

Teacher: Moritz Diehl
Assistant: Armin Nurkanivic
general:

Compulsory Elective in Mathematics (BSc21)

Teacher: Moritz Diehl
Assistant: Armin Nurkanivic
general:

Compulsory Elective in Mathematics (BSc21)

Teacher: Moritz Diehl
Assistant: Florian Messerer
general:

Compulsory Elective in Mathematics (BSc21)

Teacher: Moritz Diehl
Assistant: Florian Messerer
general:

Compulsory Elective in Mathematics (BSc21)

Teacher: Moritz Diehl
Assistant: Florian Messerer
general:

Compulsory Elective in Mathematics (BSc21)
Supplementary Module in Mathematics (MEd18)

Teacher: Moritz Diehl
Assistant: Florian Messerer
general:

Compulsory Elective in Mathematics (BSc21)

Teacher: Moritz Diehl
Assistant: Florian Messerer
general:

Time and place

Do, 10-12h, HS II, Albertstr. 23b

Teacher: Moritz Diehl
general:

Compulsory Elective in Mathematics (BSc21)
Supplementary Module in Mathematics (MEd18)

Teacher: Moritz Diehl
general:

Compulsory Elective in Mathematics (BSc21)

Teacher: Moritz Diehl
general:

Time and place

Di, 14-16h, HS II, Albertstr. 23b

Teacher: Moritz Diehl
general:

Compulsory Elective in Mathematics (BSc21)

Teacher: Moritz Diehl
general:

Compulsory Elective in Mathematics (BSc21)

Teacher: Moritz Diehl
general:

Teacher: Moritz Diehl
general:

Compulsory Elective in Mathematics (BSc21)