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Math revolution: Bonn is researching the future of linear optimization!
On May 8, 2025, the University of Bonn discussed advances in linear optimization and the interdisciplinary exchange of research.
Math revolution: Bonn is researching the future of linear optimization!
On May 8, 2025, the University of Bonn highlighted developments in mathematical optimization as part of an interdisciplinary symposium. This discipline, which has been central since the 1940s, has become particularly relevant due to the growing demands on modern digital applications that require more sophisticated computing methods. The symposium was opened by Prof. László Végh, who explained the different facets of linear optimization and its importance in today's world in his inaugural lecture entitled “The Discrete and Continuous Sides of Linear Optimization”.
In his talk, Prof. Végh explained that linear optimization, also known as linear programming, is a basic mathematical model consisting of an objective function and a set of restrictions. These models are used in a variety of application scenarios, including transportation, deployment, contract and workforce planning. While optimal solution methods, such as the well-known simplex method, have been developed since the 1960s, the theoretical complexity of finding solutions remains challenging. Nevertheless, advances in software and hardware technology have significantly improved solution speeds.
Advances in mathematical optimization
The applications of linear optimization are broad. Typical problems include maximizing an objective function or minimizing costs, often in resource-constrained settings. An example of a linear optimization model could look like this:
| goal | Restrictions |
|---|---|
| max z = 2×1 + 1.5×2 | 2×1 + x2 ≤ 1000 |
| x1 + x2 ≤ 800 | |
| x1 ≤ 400 | |
| x2 ≤ 700 | |
| x1, x2 ≥ 0 |
The methods for solving such problems have also evolved over time. Particularly noteworthy are the dual simplex method and the inner point method, which are becoming increasingly important. The performance of these methods makes it possible to effectively solve large optimization problems with up to 12 million variables, such as those found in logistics and transportation. A variety of commercial and open source solvers support the practical application of these mathematical models.
Interdisciplinary collaboration and research
As part of the symposium, the TRA speakers Prof. Dr. Alexander Effland and Prof. Dr. Jürgen Gall the relevance of interdisciplinary collaboration in this research area. They emphasized that the interfaces between mathematics, computer science and economics help to develop innovative solutions. The goals include expanding the interdisciplinary area as well as promoting future projects and networking events.
Another important aspect of mathematical optimization is the different model classes and optimization methods that are tailored to different applications. For example, methods such as branch-and-bound or branch-and-cut are used in mixed integer optimization. This diversity underlines the broad applicability of optimization in a wide variety of areas, including mathematics, computer science and complex economic issues such as those in Wikipedia are set out.
In summary, it can be said that mathematical optimization, especially linear programming, will continue to play a key role in solving complex problems in a wide variety of industries. The developments, which are driven in particular by the transdisciplinary research area at the University of Bonn, not only serve theory, but also have practical applications that can be crucial in the everyday life of companies and institutions.