I was wondering to know whether Dijkstra's algorithm can find the optimal solution for a weighted and directed shortest paths problem where: 1) for each arc $(i,j)$, $i>j$ and 2) it is not always possible to go from vertex $i$ to vertex $j$ if $i>j$ (some other constraints should be satisfied too). Note that vising all vertices is not mandatory; we just need to go from vertex $0$ to vertex $T$ (while respecting the problem constraints.)
Thanks.