A Counterexample to H. Arsham’s “initialization of the Simplex Algorithm: an Artificial-free Approach”∗
نویسندگان
چکیده
In “An artificial-free simplex-type algorithm for general LP models” [Math. Comput. Model., 25 (1997), pp. 107–123] and “Initialization of the simplex algorithm: An artificial-free approach” [SIAM Rev., 39 (1997), pp. 736–744], Arsham presents a new Phase 1 algorithm for the simplex method of linear programming, which allegedly obviates the use of artificial variables. He claims in [SIAM Rev., 39 (1997), pp. 736–744] that the new algorithm will terminate successfully or indicate the infeasibility of the problem after a finite number of iterations, and states in [Math. Comput. Model., 25 (1997), pp. 107–123] that the number of iterations is at most number of constraints. Providing this claim is true, we point out some consequences of the complexity of the simplex method. We give a counterexample, in which Arsham’s algorithm declares the infeasibility of a feasible problem.
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