An ellipsoid algorithm for the optimum design of magnetostatic problems

An ellipsoid algorithm for solving nonlinear programming problems is described whose objective and constraint functions are convex and are not assumed to be differentiable. The authors suggest some modifications to the basic ellipsoid algorithm to adapt it to magnetostatic applications. One way to do this is to control the new ellipsoid at each iteration to generate small ellipsoids and to speed up the basic algorithm. Illustrative examples show the applicability of the method to solving constrained nonlinear optimization problems in magnetostatics