Last month we took a look at quasi-Newton multivariate function minimisation algorithms which use approximations of the Hessian matrix of second partial derivatives to choose line search directions. We demonstrated that the BFGS rule for updating the Hessian after each line search maintains its positive definiteness if they conform to the Wolfe conditions, ensuring that the locally quadratic approximation of the function defined by its value, the vector of first partial derivatives and the Hessian has a minimum.

Now that we've got the theoretical details out of the way it's time to get on with the implementation.

Now that we've got the theoretical details out of the way it's time to get on with the implementation.

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