Minimizing eq. () with gradient descent is the least sophisticated but nevertheless in many cases a sufficient method. It amounts to updating the weights according to the back-propagation ( BP) learning rule 
Here refers to the whole vector of weights and thresholds used in the network.
A momentum term is often also added to stabilize the learning
Initial ``flat-spot'' problems and local minima can to a large extent be avoided by introducing noise to the gradient descent updating rule of eq. (). This is conveniently done by adding a properly normalized Gaussian noise term 
which we refer to as Langevin updating, or by using the more crude non-strict gradient descent procedure provided by the Manhattan  updating rule