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In recent years, many modern optimization techniques have been developed in the field of mathematical programming. The feasibility of applying these techniques to the magnetostatic design problems such as a permanent magnet synchronous machine and a magnetic actuator is discussed, and an improvement in the optimization method of the moving asymptotes (MMA) is suggested. The improvement of the latter consists in using an active constraint set strategy, in order to make it possible to find feasible points during the process. Theoretical aspects are considered, and numerical results of some problems are discussed.