Optimization problems with concentration and oscillation effects: relaxation theory and numerical approximation
Martin Kruzik and Tomas Roubicek
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Submission date: 01. Dec. 1998
published in: Numerical functional analysis and optimization, 20 (1999) 5-6, p. 511-530
MSC-Numbers: 49J15, 49N25, 65K10
Keywords and phrases: optimal control, impulse control, oscillations, concentrations, young measure, diperna-madja measures, weak l1-compactness, numerical approximation
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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.