The Research Unit of Variational Analysis, Dynamics and Operations Research, in the Institute of Statistics and Mathematical Methods in Economics at TU Wien is offering a position as university assistant prae-doc (all genders), for 30 hours/week, limited to expected 4 years. Earliest potential start date is April 2026.

Full details on this post and the application process can be found on the TU Wien jobs portal, opens an external URL in a new window

In addition to the above TU Wien position, VADOR has recently secured funding for a joint project with colleagues in France (ANR-FWF) and is looking to find two suitably qualified individuals to work on the proposed PhD theses.  For both positions, it is anticipated that the selected students will be based in Vienna for one half of the study period and the other half at the appointed partner University (Univ Brest or INSR Rennes) in France.  The default language of communication is English.  This research project is part of the French-Austrian International Collaborative Research Project ANR SABOCPR / FWF PIN 4368225.  Applications from suitable candidates can be sent at your earliest convenience to vador@tuwien.ac.at, opens an external URL in a new window

Theses Proposal 1 - Stability of optimal control with long time horizon

This PhD project is focused on the optimal control of ordinary differential equations (ODEs). The objective is to identify a control input that minimizes a specific cost functional over a family of system trajectories. The Pontryagin maximum principle establishes necessary conditions for optimality. A central challenge which is a key focus of this project is to analyze the stability of the maximum principle’s results under perturbations of the initial data. The proposed research concerns the investigation of the stability of the mentioned necessary conditions when the time interval where the problem is stated is very long. A typical example is the case when the cost is the (Cesaro) mean of a given function on a time interval [0, T ] and the horizon T tends to infinity. This will be the starting problem of the thesis. Several other interesting ques- tions will be investigated depending on the progress of the PhD student. Beyond the main focus, the project explores two additional areas. First, it investigates optimal control problems involving state constraints, where the regularity of solutions is a little-studied topic. Second, the research extends to non-convex cases; although stability in convex control sets is nowadays well understood, the non-convex situation requires further analysis. The work may also consider connections with Hamilton-Jacobi-Bellman equations. Since the maximum principle is expressed as a generalized equation whose stabil- ity is often analyzed using metric regularity, and considering that the resulting optimization problems are nonsmooth, the PhD candidate will need to under- stand and apply principles of nonsmooth and variational analysis to the field of optimal control.

This research project is part of the French-Austrian International Collaborative Research Project ANR SABOCPR / FWF PIN 4368225. The 3-year doctoral contract will be carried out at the TU Wien, Austria. It is expected that the PhD student spends half of his/her/their PhD journey at the TU Wien and the other half at the Université de Bretagne Occidentale, Brest, France.

Theses Proposal 2 - PDE and metric aspects of nonlocal operators 

This PhD project centers on the study of Hamilton Jacobi Bellman equations, with particular emphasis on the theory of viscosity solutions and infinite-horizon control problems. It also investigates several components of weak KAM theory, including its extension to general metric spaces, as well as abstract notions of descent such as the De Giorgi slope, global slope, and various notions of average slope. A central aim of the project is to develop and clarify the connections between these different frameworks. The proposed research concerns the investigation of appropriate notions of vis- cosity solutions for abstract descent moduli, with special focus on existence, uniqueness and stability of solutions. This corresponds to the starting point of the thesis. Further, and depending on the progresses of the PhD candidate, there are two proposed lines of research. First, due to the fact that the no- tion of viscosity solution was developed to solve Hamilton Jacobi equations, the link between descent moduli and Hamilton-Jacobi equations defined in general metric spaces can be further investigated. Second, connections between the (nonlocal) fractional Laplace equation and global slopes has been investigated. It is interesting to study asymmetric versions of the above operator from both, a PDE and a purely metric viewpoints. Some connections with a nonlocal Tug-of-war game could be also addressed. The main tools to be developed in this project are the ones of viscosity theory to tackle problems from a PDE point of view, and also the ones of variational analysis to deal with problems in the metric case.

This research project is part of the French-Austrian International Collaborative Research Project ANR SABOCPR / FWF PIN 4368225. The 3-year doctoral contract will be carried out at the Université de Rennes, France. It is expected that the PhD student spends the half of his/her/their PhD journey at the Université de Rennes and the other half at the TU Wien, Austria