VADOR Events Calendar

Our team is constantly involved in research projects, frequently involving collaboration with international scientists and institutions. Research is carried out in a number of languages, however we present mostly in English.

We frequently host one off lectures on topics relating to variational analysis, dynamics and operations research.  In term-time, we host different speakers at our weekly AKOR seminar.  Seminars take place most Thursdays at 3pm in Sem. R. DB gelb 04.  Once a month, the AKOR seminar will be replaced by the Vienna Seminar on Optimization, opens an external URL in a new window - a joint venture with Radu Bot and Yurii Malitskyi of the University of Vienna

We organise the Viennese Conference on Optimal Control and Dynamic Games, typically every three years.  The next iteration - VC2025 - will take place in July 2025.  For further details on this conference, and its forerunners, please visit the VC2025, opens an external URL in a new window website.

Topics and speakers for all forthcoming events will be posted below.

11. April 2024, 15:30 until 18:00

AKOR Seminar: Characterizing order isomorphisms of sup-stable function spaces: continuous, Lipschitz, c-convex, and beyond.. via inf/sup irreducibility

Seminar

Pierre-Cyril Aubin, TU Wien

There has been many parallel streams of research studying order isomorphisms of some specific sets G of functions over a set X, such as convex or Lipschitz functions. I will give in this talk a unified abstract approach inspired by c-convex functions. The results are obtained highlighting the role of inf and sup-irreducible elements of G and the usefulness of characterizing them, to subsequently derive the structure of order isomorphisms, and in particular of those commuting with the addition of scalars. You will see that in many cases all the (max,+)-isomorphisms J:G->G are of the form Jf=g+f\circ \phi with g:X->R and \phi:X->X bijective. We apply our theory to the sets of c-convex functions on compact Hausdorff spaces, to the set of lower semicontinuous (convex) functions on a Hausdorff topological vector space and to Lipschitz and 1-Lipschitz functions of (weak) metric spaces with compact balls. We encompass in this way many results of Artstein-Avidan and Milman, Sanchéz and Sanchéz, Leung, and others. This is a joint work with Stéphane Gaubert (INRIA, France).

Calendar entry

Event location

Sem. R. gelb 04
1040 Wien

 

Organiser

VADOR
vador@tuwien.ac.at

 

Public

No

 

Entrance fee

No

 

Registration required

No

AKOR Seminar: Characterizing order isomorphisms of sup-stable function spaces: continuous, Lipschitz, c-convex, and beyond.. via inf/sup irreducibility

Pierre-Cyril Aubin, TU Wien

There has been many parallel streams of research studying order isomorphisms of some specific sets G of functions over a set X, such as convex or Lipschitz functions. I will give in this talk a unified abstract approach inspired by c-convex functions. The results are obtained highlighting the role of inf and sup-irreducible elements of G and the usefulness of characterizing them, to subsequently derive the structure of order isomorphisms, and in particular of those commuting with the addition of scalars. You will see that in many cases all the (max,+)-isomorphisms J:G->G are of the form Jf=g+f\circ \phi with g:X->R and \phi:X->X bijective. We apply our theory to the sets of c-convex functions on compact Hausdorff spaces, to the set of lower semicontinuous (convex) functions on a Hausdorff topological vector space and to Lipschitz and 1-Lipschitz functions of (weak) metric spaces with compact balls. We encompass in this way many results of Artstein-Avidan and Milman, Sanchéz and Sanchéz, Leung, and others. This is a joint work with Stéphane Gaubert (INRIA, France).