Modern digital applications often require increasingly sophisticated calculation methods in order to deliver optimal results. Linear optimization, also known as linear programming, is a key underlying mathematical model developed back in the 1940s, with a wide range of applications in practice - for example in transport, order, event or personnel deployment planning. While efficient solution methods are already available, the ultimate theoretical complexity of the problem solution, the question of how fast an optimal solution can be found, remains open.
In his inaugural lecture entitled ‘The Discrete and Continuous Sides of Linear Optimization’, Professor László Végh gave an overview of classic results and current developments in the field of linear optimization and also presented the long-term goal: the development of so-called strongly polynomial algorithms. With these, the computing time can be limited solely by the number of variables and constraints - regardless of how large the numbers in the model are. A possible step towards calculating the optimal solution. Progress in this area is made possible by combining two central areas of optimization: discrete optimization, which aims to find the best solution from a finite or countable number of possibilities, and continuous optimization, which works with continuous values: Here, the selection for the problem solution must be made from an infinite number of possibilities.
The subject has fascinated Professor Végh for a long time, he says: “Since my childhood, I have been fascinated by mathematics and by thinking about problems. In linear programming, we are solving geometric problems in high dimensions. I remember first hearing about these problems in high school and trying to wrap my head around it. Ever since then, I have been amazed by the beauty of some of these optimization questions and the combinatorial structures in graphs and networks. These problems are an infinite source of deep and interesting questions. “
The extended program of the symposium consisted of lectures by invited guests, both international researchers and scientists from the University of Bonn. They provided an overview of the diversity of current research topics in the field and especially at the interfaces between the areas of mathematics, computer science, game theory and economics.
This overarching approach is also important for the university's Transdisciplinary Research Area (TRA) Modelling, in which Professor Végh's Hertz Chair is located: ‘We hope that the newly appointed Hertz professorship will enable the university and TRA Modelling to forge a stronger link between optimization in mathematics, computer science and economics - in particular through close links with the research strengths already established at the University of Bonn. The aim is to further expand this interdisciplinary area and to work specifically towards future joint initiatives, projects and networking events,’ explain the TRA spokespersons Professor Alexander Effland and Professor Jürgen Gall.
The symposium was a successful start to László Végh's work - full of enthusiasm for the complex questions and problems and anticipation of everything that can come out of it. An inexhaustible source of profound questions and solutions.
