Advanced Mathematical Models & Applications
Advanced Mathematical Models & Applications is a peer-reviewed, open access journal meant to publish original and significant results and articles in all areas of mathematical modeling and their applications. The aim of this Journal is to bring together researchers and practitioners from academia and industry to establishing new collaborations in this area. The Journal will consider for publication also review articles, literature reviews, correspondence concerning views and information published in previous issues.
On Comparing Pontryagin's Maximum Principle with The Basic Necessary Conditions of Variational Calculus
- Published: 03-12-2025
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This article provides a detailed comparison of Pontryagin's maximum principle with the basic necessary conditions of the classical variational calculus. Through a specific analysis and a concrete example, it is shown that, apart from the Euler equation, the more general formulations of the Weierstrass and Legendre conditions, as well as the Weierstrass-Erdmann and Jacobi conditions, are not consequences of Pontryagin's maximum principle. Hence, it can be stated that the Weierstrass-Erdmann conditions are not a consequence of Pontryagin's maximum principle. Therefore, Jacobi's condition is not a consequence of Pontryagin's Maximum Principle, and vice versa.
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