This article is a gentle stroll through the field of optimization and optimal control, aiming to acquaint the reader with the evolution of developments leading up to the Pontryagin maximum principle. The exposition adheres to simplicity without sacrificing integrity. The continuous versions of results are derived as limits of discrete versions, thus adopting a unified approach to finite-dimensional and function spaces, and wherever permissible, an intuitive connection to physics is established. Complete proofs are not provided; instead, the key geometric ideas in the proofs are presented.
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Banavar et al. (2026) studied this question.
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