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Cone-Cutting: A Variant Representation Of Pivot In Simplex

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    (Research Center on Fictitious Economy and Data Science, Chinese Academy of Sciences, Beijing, 100080, China)

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    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.

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    Article provided by World Scientific Publishing Co. Pte. Ltd. in its journal International Journal of Information Technology and Decision Making.

    Volume (Year): 10 (2011)
    Issue (Month): 01 ()
    Pages: 65-82

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    Handle: RePEc:wsi:ijitdm:v:10:y:2011:i:01:p:65-82
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