Invited Session Fri.2.H 2035

Friday, 13:15 - 14:45 h, Room: H 2035

Cluster 24: Variational analysis [...]

Optimization in infinite dimensional spaces

 

Chair: Alexander Zaslavski

 

 

Friday, 13:15 - 13:40 h, Room: H 2035, Talk 1

Joël Blot
Discrete-time Pontryagin principles and ordered Banach spaces

 

Abstract:
We provide new Pontryagin principles in infinite horizon and discrete time for systems governed by a difference inequality, xt+1 ≤ ft(xt,ut), where the order is defined by a cone in an infinite-dimensional Banach space. To obtain our results, we use a method of reduction to finite horizon, and special properties of ordered Banach spaces.

 

 

Friday, 13:45 - 14:10 h, Room: H 2035, Talk 2

Tzanko Donchev
Runge-Kutta methods for differential equations with variable time of impulses

Coauthors: Robert Bair, Qamar Din

 

Abstract:
In the paper Runge-Kutta methods of order p are used to approximate
the solutions of differential equations with variable times of impulses
in general form. We prove that under natural assumption these
methods have order of approximation O(hp). Illustrative examples
are provided. Several strategies to find the jump point of the
approximate solution for order two and four Runge-Kutta methods are
tested. The models studied can be applied in some control problems
of population dynamics and mathematical economics.

 

 

Friday, 14:15 - 14:40 h, Room: H 2035, Talk 3

Elena Resmerita
A discrepancy principle for the augmented Lagrangian method

Coauthors: Klaus Frick, Dirk Lorenz

 

Abstract:
The augmented Lagragian method received much attention recently (also under the name Bregman iteration), as an approach for regularizing inverse problems. This work shows convergence and convergence rates for this method when a special a posteriori rule, namely Morozov's discrepancy principle, is chosen as a stopping criterion. As potential fields of application we study implications of these results for particular examples in imaging, that is total variation regularization as well as lq penalties with q ∈ [1,2].

 

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