A modern survey of state-of-the-art linear programming (LP) variants. It starts with LP fundamentals, presenting right from the beginning some geometrical aspects of one of the fesible regions involved in an LP, along with the usual primal and dual simplex methods. Critical aspects such as sparse implementations, parametric and decomposition issues are dealt with, and some considerations on primal-dual, interior-point methods and integer programs are included as well. But the actual difference with standard LP books relies on the second part (entitled advanced topics) of the book, devoted to a complete analysis of both primal and dual pivoting rules and Phase-I, a promising so-called reduced simplex (in its standard, improved, D- and bounded flavours, with a strong conection with single artificial-variable Phase-I and Balinski-Tucker tableaux) and criss-cross variants, along with not-so-well-known variants as deficient-basis (to be able to deal with non-square basis matrices) in a simplex context, and face pivotal in an interior-point context. A final chapter with a wealth of even newer experimental ideas close this superb book, whose 2nd edition will see the light of day in 2022.

https://doi.org/10.1007/978-3-642-40754-3

P-Q. Pan (2014), Linear Programming Computation. Springer-Verlag, ISBN 9783662514306.

Pablo Guerrero-Garcia

University of Malaga