Dynamic Programming Perspective
From a dynamic programming point of view, Dijkstra's algorithm is a successive approximation scheme that solves the dynamic programming functional equation for the shortest path problem by the Reaching method.
In fact, Dijkstra's explanation of the logic behind the algorithm, namely
Problem 2. Find the path of minimum total length between two given nodes and .
We use the fact that, if is a node on the minimal path from to, knowledge of the latter implies the knowledge of the minimal path from to .
is a paraphrasing of Bellman's famous Principle of Optimality in the context of the shortest path problem.
Read more about this topic: Dijkstra's Algorithm
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