Newton's method can be used to find a minimum or maximum of a function.
They were the key in creating the best-known algorithm for finding a minimum spanning tree to date.
Prim's purpose is to find a minimum spanning tree for a graph.
The currently available algorithms are sub-optimal as they can only guarantee finding a local minimum, rather than a global minimum of the cost function.
The diagram above illustrates a single step in the technique for finding a minimum.
Finding a minimum or maximum weight basis of a weighted matroid, using a greedy algorithm.
By that time, the system finds a very deep (hopefully, the global one) minimum and settles there.
They were used to achieve the best complexity to date for finding a minimum spanning tree.
To find a local minimum of a function, one does line search along one coordinate direction at the current point in each iteration.
It can be seen as a modification of Newton's method for finding a minimum of a function.