4 The Revised Simplex Method and Bounded Variables
The tableau updates every entry of \(B^{-1}A\) at every pivot, although a pivot needs only one column of it, the entering one, and one row of reduced costs. For a problem with thousands of constraints and a sparse matrix \(A\), recomputing only what is needed from a factorisation of \(B\) is faster by orders of magnitude, and numerically safer. This is the revised simplex method, the form in which the simplex method is actually implemented. This section derives it, and then extends the method to variables with upper bounds, which are handled implicitly instead of as extra constraints.
4.1 The revised simplex method
4.2 Bounded variables
4.3 Numerical practice
4.4 Revised methods in software
4.5 Practice Problems
4.2 Bounded variables
4.3 Numerical practice
4.4 Revised methods in software
4.5 Practice Problems
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