Polyhedral function constrained optimization problems

Abstract

Recently polyhedral functions have proved distinctly useful in expressing selection criteria in various model building techniques. Here they play the role of a constraint on an estimation problem. Whereas they can always be replaced by an appropriate family of linear constraints, the resulting set can be a very large. Compact representations are available and their use is illustrated by developing both active set and homotopy algorithms for the general polyhedral constrained problem. These are illustrated using some well known data sets.