Function minimization methods fall on a continuum. The distinguishing characteristic is the amount of information about the function which must be explicitly calculated and supplied for the algorithm. All methods require the ability to calculate the value of the function given a particular set of values for the parameters of the model. There are methods which require only the function values (Simulated Annealing is such a method, it uses the gradient of the function only incidentally in generating new sets of parameters.). Some methods require gradient of the function as well. These methods, as a class, are called Gradient Descent methods.
The method of minimization which uses the gradient and all of the second derivative (or curvature) information is call the ``Full-Matrix'' method. The Full-Matrix method is quite powerful but the requirements of memory and computations for its implementation are beyond current computer technology except for small molecules and smaller proteins. Also, for reasons to be discussed, this algorithm can only be used when the model is very close to the minimum -- closer than most ``completely'' refined protein models. For proteins, it has only been applied to cases where the molecule is small (< 1000 atoms) which diffract to high resolution and have previously been exhaustively refined with gradient descent methods.