Comparative analysis of optimization methods for magnetostatics

A comparative analysis of the zeroth, first, and (pseudo) second-order optimization methods for n-parametric optimization of magnet systems is reported. The following families of optimization methods are compared: Monte-Carlo iteration, steepest descent, conjugate gradient, and quasi-Newton (DFP, BFGS). These methods were tested for a large class of magnetostatic optimization problems (global, nonlinear, nonconvex, constrained, discontinuous), associated, e.g. with the coil magnet design for NMR imaging and NMR spectroscopy.