Simplicial Algorithms for Minimizing Polyhedral Functions

This book, first published in 2001, provides a general account of the development of simplicial algorithms.

M. R. Osborne (Author)

9781107403505, Cambridge University Press

Paperback / softback, published 15 September 2011

262 pages
22.9 x 15.2 x 1.5 cm, 0.39 kg

Review of the hardback: 'The treatment is mathematical (definition, lemma, theorem, proof type of text) but attention is paid to algorithms and practical implementation aspects too. It is easy to read and a reference book for novice students as well as for implementors of the methods.' Bulletin of the Belgian Mathematical Society

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.

1. Some basic convex analysis
2. Introduction to Polyhedra functions
3. Linear programming algorithms
4. Piecewise linear separable problems
5. Rank regression problems
6. Polyhedral constrained optimization.

Subject Areas: Applied mathematics [PBW], Optimization [PBU], Numerical analysis [PBKS]