Geodesic
Time average optimization of cycle process with profit and effort discounts
Russian journal of nonlinear dynamics, Tome 6 (2010) no. 1, pp. 151-158.

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We prove the existence of solution in the problem of time averaged optimization of cyclic processes with both profit and effort discounts and find the respective necessary optimality condition. It is shown that optimal strategy could be selected piecewise continuous if a differentiable profit density has a finite number of critical points. In such a case the optimal motion uses only maximum and minimum velocities as in Arnold's case without any discount.
Keywords: average optimization; periodic process; necessary optimality condition; discount. 
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A. A. Davydov; T. S. Shutkina. Time average optimization of cycle process with profit and effort discounts. Russian journal of nonlinear dynamics, Tome 6 (2010) no. 1, pp. 151-158. http://geodesic.mathdoc.fr/item/ND_2010_6_1_a9/

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