Powell's Method Algorithm

Powell's method, more precisely Powell's conjugate direction method, is an algorithm proposed by Michael J. D. Powell for finding a local minimum of a real-valued function of a fixed number of real-valued inputs, without requiring the function to be differentiable and without taking any derivatives. Starting from an initial point and a set of search vectors, typically the normals aligned to each axis, the method minimizes the function through a bi-directional line search along each search vector in turn, using a technique such as golden-section search or Brent's method for each line search; it is useful for finding the local minimum of a continuous but complex function that lacks an underlying mathematical definition, since no derivatives are required.