Geodesic
Problems and Methods of Averaged Optimization
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Differential equations and dynamical systems, Tome 261 (2008), pp. 276-292.

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Typical extremal problems containing the mean values of unknowns or of some functions of unknowns are considered. Relationships between these problems and cyclic modes of dynamical systems are revealed, and optimality conditions for such modes are found. 
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A. M. Tsirlin. Problems and Methods of Averaged Optimization. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Differential equations and dynamical systems, Tome 261 (2008), pp. 276-292. http://geodesic.mathdoc.fr/item/TM_2008_261_a21/

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