Dual formulation of the Pontryagin maximum principle in optimal control
Informatics and Automation, Optimal control, Tome 291 (2015), pp. 69-75.

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An invariant dual formulation of the Pontryagin maximum principle is given for the time-optimal case.
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R. V. Gamkrelidze. Dual formulation of the Pontryagin maximum principle in optimal control. Informatics and Automation, Optimal control, Tome 291 (2015), pp. 69-75. http://geodesic.mathdoc.fr/item/TRSPY_2015_291_a5/

[1] Pontryagin L.S., Boltyanskii V.G., Gamkrelidze R.V., Mischenko E.F., Matematicheskaya teoriya optimalnykh protsessov, Fizmatgiz, M., 1961