Our aim with this part of the project is to be able to

• find an optimal value for the variational parameters using only some few Monte Carlo cycles
• use these optimal values for the variational parameters to perform a large-scale Monte Carlo calculation

To achieve this will look at methods like the simplest possible gradient descent, Steepest descent, the conjugate gradient method and stochastic gradient descent. These methods allow us to find the minima of a multivariable function like our energy (function of several variational parameters). Alternatively, you can always use Newton's method. In particular, since we will normally have one variational parameter, Newton's method can be easily used in finding the minimum of the local energy.