Cone-Cutting: A Variant Representation Of Pivot In Simplex

This study presents a variant representation of pivot in simplex, which performs cone-cutting on a coneCin dual space to match the pivot performed on a basisB, while the edge-vectors ofCare indicated by the row vectors of the feature matrixF = B-1in the simplex table. Under this representation, we can see the dual coneCof basisBthrough the feature matrixFdirectly, and we can perform pivot motivated by the monitor viewing toward the dual space. As an example, a constraint plane in the dual space is delete-able for the optimal searching if it does not pass through the dual optimal point, while such a plane corresponds to a variable being not in the optimal basis. Motivated by the cone-cutting's vision, a variable-sifting algorithm is presented in Sec. 3, which marks those variables corresponding to delete-able planes into a list to forbid them enter pivot and put zero to their components in the final solution.