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

Hamdy A. Taha and Guy L. Curry
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Hamdy A. Taha: University of Arkansas, Fayetteville, Arkansas
Guy L. Curry: University of Arkansas, Fayetteville, Arkansas

Operations Research, 1971, vol. 19, issue 4, 1045-1050

Abstract: 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 ( c j − z j ) for nonbasic variables x j must be nonpositive (nonnegative) in order for a maximization (minimization) linear program to be optimal.

Date: 1971
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