Geometric approach to Fletcher's ideal penalty function

Original article can be found at: www.springerlink.com Copyright Springer. [Originally produced as UH Technical Report 280, 1993]In this note, we derive a geometric formulation of an ideal penalty function for equality constrained problems. This differentiable penalty function requires no parameter estimation or adjustment, has numerical conditioning similar to that of the target function from which it is constructed, and also has the desirable property that the strict second-order constrained minima of the target function are precisely those strict second-order unconstrained minima of the penalty function which satisfy the constraints. Such a penalty function can be used to establish termination properties for algorithms which avoid ill-conditioned steps. Numerical values for the penalty function and its derivatives can be calculated efficiently using automatic differentiation techniques.Peer reviewe

Inelastic neutron scattering study on the resonance mode in an optimally doped superconductor LaFeAsO0.92_{0.92}F0.08_{0.08}

An optimally doped iron-based superconductor LaFeAsO$_{0.92}$F$_{0.08}$ with $T_c = 29$ K has been studied by inelastic powder neutron scattering. The magnetic excitation at $Q=1.15$ \AA$^{-1}$ is enhanced below $T_c$, leading to a peak at $E_{res}\sim13$ meV as the resonance mode, in addition to the formation of a gap at low energy below the crossover energy $\Delta_{c}\sim10 meV$. The peak energy at $Q=1.15$ \AA$^{-1}$ corresponds to $5.2 k_B T_c$ in good agreement with the other values of resonance mode observed in the various iron-based superconductors, even in the high-$T_c$ cuprates. Although the phonon density of states has a peak at the same energy as the resonance mode in the present superconductor, the $Q$-dependence is consistent with the resonance being of predominately magnetic origin.Comment: 4 pages, 5 Postscript figure