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MiS Preprint
57/1998

Optimization problems with concentration and oscillation effects: relaxation theory and numerical approximation

Martin Kruzik and Tomas Roubicek

Abstract

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:
Dec 1, 1998
Published:
Dec 1, 1998
MSC Codes:
49J15, 49N25, 65K10
Keywords:
optimal control, impulse control, oscillations, concentrations, young measure, diperna-madja measures, weak l1-compactness, numerical approximation

Related publications

inJournal
1999 Repository Open Access
Martin Kružík and Tomas Roubicek

Optimization problems with concentration and oscillation effects: relaxation theory and numerical approximation

In: Numerical functional analysis and optimization, 20 (1999) 5-6, pp. 511-530