Gradient Descent algorithms converge to a local minimum, and if the function is convex, they converge to a __________ minimum.

In the context of optimization, particularly when discussing gradient descent algorithms, it's important to understand the properties of the functions being optimized. Gradient descent is an iterative method used for finding the minimum of a function. It works by descending down the gradient of the function to reach the lowest point.

When a function is convex, it possesses the property that any line segment joining two points on the function lies above or on the graph of the function. This characteristic ensures that the function has a single global minimum. Therefore, when gradient descent is applied to a convex function, it will converge to the global minimum.

So, completing the statement:

Gradient Descent algorithms converge to a local minimum, and if the function is convex, they converge to a global minimum.