In the work are considered the basic features of the most characteristic magnetic systems of electromagnetic devices. Described position of task for optimization of the mentioned devices: scopes of the optimized system, choice of characteristic criterion, choice of intersystem variables, and construction of mathematical model. In more detail are described optimization problems of one-dimensional task, in view of nonlinear characteristics of the ferromagnetic materials, applied in electromagnetic devices. It is shown, that at the decision of similar problems of optimization most effective is the method of exception of intervals at a half division. Described the algorithm of such method and direct the block diagram.