How Much Optimal Dilation Improves on the Classical Solution|the Canonical Connguration

from which numerical optimization of r is commenced|with respect to (i) the value of r and (ii) the probability of converging to a global minimizer of r. We expect to address these issues empirically, by extensive computational experimentation, but we have some hope of a theoretical analysis in the comparatively tractable case of 2. 3. How can Theorem 1 be exploited for global optimization? It is apparent from Theorem 1 that the stationary conngurations of r have considerable structure. Furthermore, part (iii) of Theorem 1 suggests a strategy for globally optimizing r. Because we now understand that these observations apply to any r , not just the case of r = 2 addressed by Glunt, Hayden, and Liu (1991), the potential gains from exploiting them are greatly increased.