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 cone C in dual space to match the pivot performed on a basis B, while the edge-vectors of C are indicated by the row vectors of the feature matrix F = B-1 in the simplex table. Under this representation, we can see the dual cone C of basis B through the feature matrix F directly, 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.