We offer students a profound and broad education in the field of continuous optimization. This includes introductory courses on the basics of optimization for both, students of mathematics as well as students of engineering or computer science, as well as a broad range of advanced and in-depth courses. Those cover more theoretical topics like optimization in infinite-dimensional vector spaces, but also more applied topics like algorithmic methods of optimization. In addition, we offer lectures on the basics of mathematics for business and engineering courses. For us, a high quality of teaching is important, which spans the arc from theoretical principles and scientific approaches to practical application.
Video on studying mathematics in Ilmenau with Ms. Kästner.
Video on studying mathematics in Ilmenau with Ms. Bold.
Information on the lecture programme can be found primarily in the course catalogue and on moodle.
Members of the team of the department offer in winter 2022/2023 among others:
Lecture on Nonlinear Optimization
Within this course, we study properties and solution approaches for convex optimization problems, i.e., for nonlinear optimization problems with a convex objective function and convex constraints. Besides optimality conditions of unconstrained and constrained optimization problems, numerical methods like descent methods, Newton method, or penalty approaches are discussed.
Expected audience: Students of mathematics in the 5th semester of their bachelor studies, as well as students of other fields with a sufficient background from introductory courses in math (linear algebra and analysis).
Lecturer: Prof. Eichfelder, M. Sc. Hoff
Lecture on Vector Optimization
The topic of the lecture are optimization problems where the objective function maps into a partially ordered linear space. This also includes the class of multiobjective optimization problems, where several objective functions are optimized simultaneously. A main focus of the lecture is the examination of scalarization approaches, i.e., the formulation of parameter-dependent replacement problems, which can be used to calculate optimal solutions of vector optimization problems by numerical methods. Further topics are existence results, optimality conditions, duality results, robust approaches to uncertain optimization, and set optimization.
Expected audience: Students of mathematics and business mathematics at the end of the bachelor’s programme or in the master's programme; especially suitable for preparation of a master's thesis at the department.
Lecturer: Prof. Eichfelder, M. Sc. Hoff
Lecture on Mathematics for Economics and Social Sciences 1
In this lecture, the mathematical basics for further studies in economics and social science are taught, like basic concepts of logic, properties of functions of one variable, sequences and continuity of functions, differentiation, also for multivariate functions. The lecture is continued with Mathematics for Economics and Social Sciences 2 .
Expected audience: First year students of Wirtschaftsinformatik, Betriebswirtschaftslehre mit technischer Orientierung or Medienwirtschaft in the bachelor's program
Lecturer: Prof. Eichfelder, Dr. R. Gerlach, Dr. T. Gerlach
Seminar
In this seminar the participants will present a selected topic from the current scientific literature from the field of nonlinear optimization. Each student will be given a research paper, a recent publication from a journal, and will present a selection from its content (including a proof) in a 60-90 minutes seminar talk. These presentations will be supplemented by guest lectures and presentations from the working group. Depending on the prior knowledge of the participants, the research papers of this seminar will deal with current topics from the whole range of nonlinear optimization, such as convex relaxations of nonconvex problems, robust classification approaches for data, descent methods of bilevel optimization, multiobjective or set-valued optimization.
Lecture on Mathematics for Economics and Social Sciences 2
In this lecture, the mathematical basics for further studies in economics and social science are taught, like basics of linear algebra, differentiation and the integral of multivariate functions. The lecture is based on Mathematics for Economics and Social Sciences 1.
Expected audience: First year students of Wirtschaftsinformatik, Betriebswirtschaftslehre mit technischer Orientierung or Medienwirtschaft in the bachelor's program
Lecture on Global Optimization
Numerical methods of nonlinear optimization find in general only locally optimal solutions. However, for non-convex optimization problems, there may be locally optimal points which are not also globally optimal. In global optimization approaches are developed which can also guarantee to find the global minimum value of a non-convex optimization problem. Further topics of the lecture are the reformulation of combinatorial or mixed-integer optimization problems as continuous optimization problems or as linear optimization problems over the cone of copositive matrices, and how this can be used for numerical methods.
Lecture on Optimization
The lecture provides an introduction to the field of continuous mathematical optimization. Besides basics (such as convex sets, convex functions, optimality conditions of unconstrained and constrained optimization) the lecture focuses on linear optimization problems.
Expected audience: Students of computer science with mathematics as minor subject in the 3rd semester, as well as students of other courses of study with sufficient basics from introductory mathematics lectures (linear algebra and analysis)
Lecture on Introduction to Operations Research and Linear Optimization
The lecture deals especially with linear optimization problems, i.e., problems where one wants to minimize a linear objective function over a polyhedron. In addition to the theoretical basics, students will learn about the two main numerical methods of linear optimization: the simplex method and the interior-point method.
Expected audience: Students of mathematics in the second semester of their bachelor studies, as well as students of other fields with a sufficient background from introductory courses in math (linear algebra and analysis)
Lecture on Mathematics 1 for Students of Industrial Engineering and Management
In this lecture, the mathematical basics for further studies in economics and engineering are taught, like basic concepts of logic, sets and maps, basics of linear algebra, properties of functions of one variable, as well as sequences of numbers. The lecture is continued with Mathematics 2 and 3.
Expected audience: First year students of industrial engineering and management in the bachelor's program
Lecture on Mathematics 2 for Students of Industrial Engineering and Management
In this lecture, the mathematical basics for further studies in economics and engineering are taught, like sequences and continuity of functions, differentiation and the integral of multivariate functions. The lecture is based on Mathematics 1 and will be continued with Mathematics 3.
Expected audience: First year students of industrial engineering and management in the bachelor's program
Lecture on Mathematics 3 for Students of Industrial Engineering and Management
In this lecture series, the mathematical basics for further studies in economics and engineering are taught, like sequences and continuity of functions, differentiation and the integral of multivariate functions. The lecture is based on Mathematics 1 and Mathematics 2 and has as main topic differential equations.
Expected audience: Second year students of industrial engineering and management in the bachelor's program