In the previous post we saw how we could perform a univariate line search for a point that satisfies the Wolfe conditions meaning that it is

*reasonably*close to a minimum and takes a lot less work to find than the minimum itself. Line searches are used in a class of multivariate minimisation algorithms which iteratively choose directions in which to proceed, in particular those that use approximations of the Hessian matrix of second partial derivatives of a function to do so, similarly to how the Levenberg-Marquardt multivariate inversion algorithm uses a diagonal matrix in place of the sum of the products of its Hessian matrices for each element and the error in that element's current value, and in this post we shall take a look at one of them.Full text...