Structured minimal-memory inexact quasi-Newton method and secant preconditioners for augmented Lagrangian optimization

Augmented Lagrangian methods for large-scale optimization usually require efficient algorithms for minimization with box constraints. On the other hand, active-set box-constraint methods employ unconstrained optimization algorithms for minimization inside the faces of the box. Several approaches may be employed for computing internal search directions in the large-scale case. In this paper a minimal-memory quasi-Newton approach with secant preconditioners is proposed, taking into account the structure of Augmented Lagrangians that come from the popular Powell-Hestenes-Rockafellar scheme. A combined algorithm, that uses the quasi-Newton formula or a truncated-Newton procedure, depending on the presence of active constraints in the penalty-Lagrangian function, is also suggested. Numerical experiments using the Cute collection are presented.

Solar Collectors for Historic Homes : Linking consumption to perceptions of space

Reduction of household energy consumption is one of the top issues in contemporary discussions on sustainable consumption. This chapter concerns one way through which consumption of purchased energy for house heating can be reduced; by having a solar thermal system added to one's house. However, the fact that one of the components - the solar collector - usually is situated on the roof or the facade of a building, is a recurrent impediment to such installations. In certain contexts, these attributes may melt into the building, while in others, they may be perceived as problematic. The latter may particularly be the case when the appearance of the building is of major imiportance, as with houses deemed worthy of preservation for coming generations. This chapter draws upon a study carried out in Visby Town, a walled Hanseatic town and a World Heritage site on the island of Gotland, Sweden.