The description of the simplex method that we have given is based on the standard form of the linear programming problem. This is the standard approach taken in most textbooks; see, for example, Chvátal [8]. The book of Gill, Murray, and Wright [19] describes the simplex method from both the classical perspective and the linearly constrained viewpoint; this book also contains background material on linear algebra. Murtagh [28] gives a more concise, handbook-style treatment. See Network Programming page for books on network linear programming problems.
The book Primal-Dual Interior-Point Methods by Stephen Wright gives a complete introduction to theoretical and practical aspects of this most useful class of interior-point methods for linear programming. The home page for this book contains links to many of the software packages of current interest, many of which are available free to researchers.
Research in interior-point methods continues at a rapid pace. The Interior-Point Methods Online web archive contains links to most of the new papers and reports in the area since December, 1994.
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Updated 1 August 1997
