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The Prepared Problem Boundedness and Consistency
Optimal Points Motivation of the Simplex Method
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active vectors arbitrarily large values bm+1 boundedness calculation called Charnes cjXj closed half-spaces coefficients column vectors components constraints are consistent convex polygon convex set define degeneracy denote dual pair dual problem Duality element empty equation exist extreme point feasible points feasible vector final tableau flux stock follows half-spaces hence hyperplane identity matrix independent intersection Lemma linear combination linear functional linear inequality linear programming linear space maximal extreme vector multiply n-component number of closed numerical example optimal point optimal vector original problem perturbed problem perturbed tableau point of F prepared problem primal problem programming problem real number row operations row vector satisfies scalar set F simplex method slack variables straints subset subspace Suppose theorem unbounded unperturbed upper bound variables vector for problem vector of FP vectors Xa whence zero