Introduction to Derivative Minimisation Methods

When discussing derivative methods it is useful to write the function as a Taylor series expansion about the point x  

For a multidimensional fimction, the variable x is replaced by the vector x and matrices are used for the various derivatives. Thus if the potential energy f (x) is a ftmction of 3N Cartesian coordinates, the vector x will have 3N components and xjt corresponds to the current configuration of the system, is a 3N x 1 matrix (i.e. a vector), each element 

The derivative methods can be classified according to the highest-order derivative used. First-order methods use the first derivatives (i.e. the gradients) whereas second-order methods use both first and second derivatives. The simplex method can thus be considered a zeroth-order method as it does not use any derivatives. 

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