A* Optimality with consistent heuristic

Question

Where can I find a proof for the following theorem:

Theorem: If h(n) is consistent, A* using GRAPH-SEARCH is optimal

Thanks.

Answer 1

First, we have to define these functions:

• g(n) = it is the cost to reach node from start node
• f(n) = g(n) + h(n)

Steps:

1. Verify that the values of f(n) along any path are nondecreasing if h(n) is consistent.
2. Confirm that whenever A* selects a node for expansion, the optimal path to that node has been found.