Geometric abstractions for constrained optimization of layouts . ∗

We discuss implementation of algorithms for constrained optimization, based on CLOS objects representing standard mathematical abstractions like affine spaces, vectors , and linear transformations. These abstractions simplify using the optimization library in varied applications, facilitate animation, carry no significant performance penalty (compared to traditional Fortran implementations). Our motivating problem is constructing layouts for interactive displays used to browse through the contents of a database (eg. a document retrieval system). These displays are constructed using ideas similar to multidimensional scaling; screen positions for glyphs representing entities in the database are chosen to minimize a penalty function that reflects the relationships among the entities.