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.

21. March 2024, 15:00 until 17:00

AKOR Seminar, Fast continuous time methods for monotone equations

Seminar

Radu Bot, University of Vienna

 

In this talk we discuss continuous in time dynamics for the problem of approaching the set of zeros of a single-valued monotone and continuous operator. Such problems are motivated by minimax convex-concave and, in particular, by convex optimization problems with linear constraints. The central role is played by a second-order dynamical system that combines a vanishing damping term with the time derivative of the operator along the trajectory, which can be seen as an analogous of the Hessian-driven damping in cases where the operator originates from a potential. We demonstrate that the norm of the operator along the trajectory and the restricted gap function exhibit fast vanishing behaviour, and that the trajectory converges weakly to a solution of the monotone equation. The implicit and explicit discrete time models, enhanced with Nesterov’s momentum and correcting terms, share the asymptotic features of the continuous dynamics. In the second part of the talk, we discuss the connection between the second-order dynamical system and a Tikhonov regularized first-order dynamical system, exhibiting fast convergence rates and strong convergence of the trajectory.

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, Fast continuous time methods for monotone equations

Radu Bot, University of Vienna

In this talk we discuss continuous in time dynamics for the problem of approaching the set of zeros of a single-valued monotone and continuous operator. Such problems are motivated by minimax convex-concave and, in particular, by convex optimization problems with linear constraints. The central role is played by a second-order dynamical system that combines a vanishing damping term with the time derivative of the operator along the trajectory, which can be seen as an analogous of the Hessian-driven damping in cases where the operator originates from a potential. We demonstrate that the norm of the operator along the trajectory and the restricted gap function exhibit fast vanishing behaviour, and that the trajectory converges weakly to a solution of the monotone equation. The implicit and explicit discrete time models, enhanced with Nesterov’s momentum and correcting terms, share the asymptotic features of the continuous dynamics. In the second part of the talk, we discuss the connection between the second-order dynamical system and a Tikhonov regularized first-order dynamical system, exhibiting fast convergence rates and strong convergence of the trajectory.