Abstract
The computation of the basis inverse is the most time-consuming step in simplex-type algorithms. The basis inverse does not have to be computed from scratch at each iteration, but updating schemes can be applied to accelerate this calculation. This chapter presents two basis inverse and two basis update methods used in simplex-type algorithms: (i) Gauss-Jordan elimination basis inverse method, (ii) LU Decomposition basis inverse method, (iii) Product Form of the Inverse basis update method, and (iv) Modification of the Product Form of the Inverse basis update method. Each technique is presented with: (i) its mathematical formulation, (ii) a thorough numerical example, and (iii) its implementation in MATLAB. Finally, a computational study is performed. The aim of the computational study is to compare the execution time of the basis inverse and update methods and highlight the significance of the choice of the basis update method on simplex-type algorithms and the reduction that it can offer to the solution time.
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Ploskas, N., Samaras, N. (2017). Basis Inverse and Update Methods. In: Linear Programming Using MATLAB® . Springer Optimization and Its Applications, vol 127. Springer, Cham. https://doi.org/10.1007/978-3-319-65919-0_7
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