Understanding the physics of nuclei at the limits of deformation. Superdeformed nuclei (i.e., nuclei with a major-to-minor axis ratio of {approximately}2:1) provide a unique laboratory for nuclear structure studies at the limits of observable deformation. Islands of superdeformation are predicted and found throughout the table of isotopes. We have focused our attention on the A = 190 region, since neutron deficient Hg and Pb nuclei were predicted to support a stable superdeformed minimum at zero angular momentum. We are making major contributions to the development of this region of superdeformation. We find general agreement with fully 3-D Hartree Fock calculations done with a microscopic interaction, including pairing. Our measurements test predictions in the second well which are based on extrapolation of nuclear theory determined at `normal` deformation. In addition, unusual phenomena are expected because of the large difference in shape between well I and well II states. Our experiments require the sensitivity and resolution of large scale Ge detector arrays.

We consider a modification of a path-following infeasible-interior- point algorithm described by Wright. In the new algorithm, we attempt to improve each new iterate by reusing the coefficient matrix factors from the latest step. We show that the modified algorithm has similar theoretical global convergence properties to the earlier algorithm, while its asymptotic convergence rate can be made superquadratic by an appropriate parameter choice.