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Classical Derivation of the Necessary and Sufficient Conditions for Optimal Linear Programs

This paper presents a new derivation of the key ideas of Dantzig's simplex algorithm by using the differential approach to nonlinear programming. Specifically, the necessary condition shows that a candidate for the optimum is a basic feasible solution, while the sufficiency condition indicates that the optimality indicator cj-zj for nonbasic variables xj must be nonpositive nonnegative in order for a maximization minimization linear program to be optimal.