Skip to main content
. Author manuscript; available in PMC: 2013 Mar 1.
Published in final edited form as: J Magn Magn Mater. 2011 Sep 19;324(5):742–754. doi: 10.1016/j.jmmm.2011.09.008

Figure 2.

Figure 2

Global optimality is proved by showing that the upper and lower bounds converge, squeezing the optimum design between them. The figure shows upper and lower bounds, as well as the sub-optimal and final optimal force value, for the Halbach optimization case of Section 6.1. At each iteration of the optimization, it is known that the true optimum magnetic force must be less than the upper bound (red line, computed by SDR) and greater than the lower bound (blue line, computed by an approximate convex optimization scheme). As the optimization proceeds, better and better solutions are found, and the bounds are driven closer together eventually converging (here at iteration 4). The shown global optimum (black dot) corresponds to a 36 element Halbach array that creates a magnetic force at a distance of 10 cm that is 71 % greater than the force created by a uniformly magnetized block of the same size and magnetic field strength.