The best location and dipole moment (six parameters in all for each dipole) are usually obtained by finding the global minimum of the residual energy, that is the L2-norm ||V in - V model ||, where V model ∈ ℝ N represents the electrode potentials with the hypothetical dipoles, and V in ∈ ℝ N represents the recorded EEG for a single time instant. This requires a non-linear minimization of the cost function ||M - G({r j , rdipi})D|| over all of the parameters (rdipi, D). Common search methods include the gradient, downhill or standard simplex search methods (such as Nelder-Mead) [43-46], normally including multi-starts, as well as genetic algorithms and very time-consuming simulated annealing [45,47,48]. In these iterative processes, the dipolar source is moved about in the head model while its orientation and magnitude are also changed to obtain the best fit between the recorded EEG and those produced by the source in the model. Each iterative step requires several forward solution calculations using test dipole parameters to compare the fit produced by the test dipole with that of the previous step.
