The paper gives an overview on mathematical optimization techniques specially suited to problems in electromagnetism. It is described how efficient optimization procedures consist of decision making, treatment of non-linear constraints, and an algorithm for minimizing the objective function. The optimization of a rectangular waveguide branching, a permanent magnet synchronous machine, and the iron cross-section of a superconducting magnet are given as examples. Optimization routines are used for the tracing of manufacturing errors in the production of superconducting coils. Finally the application of a genetic algorithm to a dipole coil design is discussed as an example for field synthesis.
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Stephan Russenschuck (1996) studied this question.