Linear Optimization and Extensions

This monograph describes linear programming as well as the optimization of linear functions over polyhedra in finite dimensional Euclidean vector spaces. An introduction surveying 50 years of linear optimization research is also provided.

---

This text offers a comprehensive treatment of linear programming as well as of the optimization of linear functions over polyhedra in finite dimensional Euclidean vector spaces. An introduction surveying 50 years of linear optimization is given. The main topics treated include simplex algorithms and their derivatives, such as the duality theory of linear programming, polyhedral theory, projective algorithms, Newtonian barrier methods, and ellipsoid algorithms in perfect and in finite precision arithmetic. The book can serve both as a graduate textbook for linear programming and as a text for advanced topics classes or seminars. Exercises as well as several case studies are included.