The paper gives an overview on mathematical optimization techniques specially suited for problems in electromagnetism. Optimization techniques include decision-making, methods to treat nonlinear constraints, and algorithms to minimize the objective function. Applications to the design of superconducting magnets for the Large-Hadron-Collider project at CERN are discussed. For the mathematical optimization of these magnets two program packages have been developed and are described in the paper. The ROXIE program is used for the optimization of coil cross-sections, inverse field problem solving and coil-end design. The POISOPT program is an extension of the finite-element program package POISSON, used for the minimization of saturation induced effects from the iron yoke of the magnets.
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