Geodesic
The Pontryagin maximum principle. Ab ovo usque ad mala
Informatics and Automation, Optimal control, Tome 291 (2015), pp. 215-230.

Voir la notice de l'article provenant de la source Math-Net.Ru

A proof of the Pontryagin maximum principle for a sufficiently general optimal control problem is presented; the proof is based on the implicit function theorem and the theorem on the solvability of a finite-dimensional system of nonlinear equations. The exposition is self-contained: all necessary preliminary facts are proved. These facts are mainly related to the properties of solutions to differential equations with discontinuous right-hand side and are derived as corollaries to the implicit function theorem, which, in turn, is a direct consequence of Newton's method for solving nonlinear equations. 
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G. G. Magaril-Il'yaev. The Pontryagin maximum principle. Ab ovo usque ad mala. Informatics and Automation, Optimal control, Tome 291 (2015), pp. 215-230. http://geodesic.mathdoc.fr/item/TRSPY_2015_291_a15/

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