Polyhedral functions provide a model for an important class of
problems that includes both linear programming and applications in
data analysis. General methods for minimizing such functions using
the polyhedral geometry explicitly are developed. Such methods
approach a minimum by moving from extreme point to extreme point
along descending edges and are described generically as simplicial.
The best-known member of this class is the simplex method of linear
programming, but simplicial methods have found important
applications in discrete approximation and statistics. The general
approach considered in this text, first published in 2001, has
permitted the development of finite algorithms for the rank
regression problem. The key ideas are those of developing a general
format for specifying the polyhedral function and the application
of this to derive multiplier conditions to characterize optimality.
Also considered is the application of the general approach to the
development of active set algorithms for polyhedral function
constrained problems and associated Lagrangian forms.
General
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