In this paper we generalize the so-called first-in-last-out pivot rule and the most-often-selected-variable pivot rule for the simplex method, as proposed in Zhang \\cite{Z91}, to the criss-cross pivot setting where neither the primal nor the dual feasibility is preserved. The finiteness of the new criss-cross pivot variants is proven.

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Keywords anti-cycling, criss-cross pivot method, linear programming
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Zhang, S.. (1997). New variants of finite criss-cross pivot algorithms for linear programming (No. EI 9707-/A). Retrieved from