Optimal shape design of iron pole section of electromagnet

In this Letter, the classical problem of determining the optimal shape of the pole of an electromagnet is considered. In order to determine the optimal shape, we have extended a measure theory-based method. The problem of finding the optimal shape is reduced to one consisting of minimizing a linear form over a set of positive measures. To do so, an embedding procedure is applied. The resulting problem can be approximated by a finite-dimensional linear programming problem. The solution of the problem is used to construct a nearly optimal shape.