MiS Preprint Repository
We have decided to discontinue the publication of preprints on our preprint server end of 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.
Optimization problems with concentration and oscillation effects: relaxation theory and numerical approximation
Martin Kruzik and Tomas RoubicekAbstract
The paper deals with optimal control problems for which minimizing (sub)sequences of controls do not converge weakly in L1. For such problems, here governed by ordinary differential equations, the relaxed (generalized) solutions in terms of DiPerna-Majda measures are defined, correctness of the relaxation is shown and a numerical approximation is developed and tested on model examples.
- Received:
- 01.12.98
- Published:
- 01.12.98
- MSC Codes:
- 49J15, 49N25, 65K10
- Keywords:
- optimal control, impulse control, oscillations, concentrations, young measure, diperna-madja measures, weak l1-compactness, numerical approximation