Powell's method, strictly Powell's conjugate direction method, is an algorithm proposed by Michael J. D. Powell for finding a local minimum of a function. The function need not be differentiable, and no derivatives are taken.

The function must be a real-valued function of a fixed number of real-valued inputs. The caller passes in the initial point. The caller also passes in a set of initial search vectors. Typically N) are passed in which are simply the normals aligned to each axis.

The method minimises the function by a bi-directional search along each search vector, in turn. The bi-directional line search along each search vector can be done by Golden-section search or Brent's method), is deleted from the search vector list. The new set of N. The algorithm iterates an arbitrary number of times until no significant improvement is made.

The method is useful for calculating the local minimum of a continuous but complex function, especially one without an underlying mathematical definition, because it is not necessary to take derivatives. The basic algorithm is simple; the complexity is in the linear searches along the search vectors, which can be achieved via Brent's method.

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