Mathematical optimization of superconducting accelerator magnets

This paper presents the mathematical optimization techniques applied in order to find the most appropriate design for the superconducting bending magnets for CERN´s new project, the Large Hadron Collider. It describes the program package ROXIE and the POISOPT routine which is an extension of the finite element program package POISSON. The nature of vector-optimization problems with a number of partly contradictory objectives for the optimal design is explained. These vector-optimization problems lead to a set of Pareto-optimal solutions from which one compromise solution has to be chosen by a decision making process. The paper describes different methods for decision making and suitable optimization procedures