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.

07. September 2023, 15:59 until 18:00

AKOR Seminar: Alternating minimization and some generalizations of convexity

Seminar

Pierre-Cyril Aubin, TU Wien

I will present my recent research in going beyond the quadratic cost in optimization, by replacing it with a general cost function. With Flavien Léger (INRIA Paris), we unveiled in arxiv.org/abs/2305.04917, opens an external URL in a new window a new class of gradient-type optimization methods that extends vanilla gradient descent, mirror descent, Riemannian gradient descent, and natural gradient descent. Our approach involves constructing a surrogate for the objective function in a systematic manner, based on a chosen cost function. This surrogate is then minimized using an alternating minimization scheme. Using optimal transport theory we establish convergence rates based on generalized notions of smoothness and convexity. We provide local versions of these two notions when the cost satisfies a condition known as nonnegative cross-curvature. In particular our framework provides the first global rates for natural gradient descent and Newton's method. For a quick read of arxiv.org/abs/2305.04917, opens an external URL in a new window I recommend reading the summary p4-6 and then look for your favorite algorithm (mirror, Riemannian, etc) in Section 4. 

Calendar entry

Event location

Sem. R. DB 04
1040 Wien

 

Organiser

VADOR
vador@tuwien.ac.at

 

More Information

https://arxiv.org/abs/2305.04917

 

Public

No

 

Entrance fee

No

 

Registration required

No

AKOR Seminar: Alternating minimization and some generalizations of convexity

Pierre-Cyril Aubin, TU Wien

I will present my recent research in going beyond the quadratic cost in optimization, by replacing it with a general cost function. With Flavien Léger (INRIA Paris), we unveiled in arxiv.org/abs/2305.04917, opens an external URL in a new window a new class of gradient-type optimization methods that extends vanilla gradient descent, mirror descent, Riemannian gradient descent, and natural gradient descent. Our approach involves constructing a surrogate for the objective function in a systematic manner, based on a chosen cost function. This surrogate is then minimized using an alternating minimization scheme. Using optimal transport theory we establish convergence rates based on generalized notions of smoothness and convexity. We provide local versions of these two notions when the cost satisfies a condition known as nonnegative cross-curvature. In particular our framework provides the first global rates for natural gradient descent and Newton's method. For a quick read of arxiv.org/abs/2305.04917, opens an external URL in a new window I recommend reading the summary p4-6 and then look for your favorite algorithm (mirror, Riemannian, etc) in Section 4.