Many modern optimization problems – from designing robust communication networks, to planning facilities in location science, to scheduling production in manufacturing systems – require careful evaluation of possible solutions. Thereby, it is often desired to rank different options by how their individual cost components compare to each other, rather than simply summing all components up. This project, a bilateral collaboration between Spanish and German universities, investigates how such ordered decision structures can be better understood and solved by combining ideas from discrete and continuous optimization.

A central theme is the study of ordered median problems, a well-established class of problems in which costs are first sorted and then weighted according to their order. These models provide a unifying framework that encompasses classical objectives such as minimizing total cost, minimizing the maximum cost, and many hybrids in between. They are particularly useful in applications where decisions must respect priorities, fairness, or efficiency considerations.

At the same time, continuous optimization is increasingly concerned with nonlinear geometric spaces, such as curved manifolds and general metric spaces, which better capture the structure of many real applications. Existing theory and algorithms are still limited in these settings, especially when discrete or combinatorial features are involved.

The project aims to strengthen the connection between discrete and continuous optimization and to extend the theoretical understanding of problems in nonlinear spaces. It also seeks to develop new modeling approaches and algorithms that leverage the unifying structure of ordered median formulations, and to create more effective exact and heuristic methods for a large variety of practical optimization problems.