The answer is False.
A complete, local search algorithm always finds a goal if one exists. However, it does not always find the global minimum or maximum. This is because local search algorithms only explore a small neighborhood of the current solution, and they may not be able to escape from local minima or maxima.
An optimal algorithm always finds the global minimum or maximum, but it may not be able to find a solution if one does not exist. This is because optimal algorithms must explore the entire search space, which can be very large in some cases.
In conclusion, a complete, local search algorithm always finds a goal if one exists, but it does not always find the global minimum or maximum. An optimal algorithm always finds the global minimum or maximum, but it may not be able to find a solution if one does not exist.