Moreover, a new, ratio-test-free pivoting rule is proposed, significantly reducing computational cost at each iteration. Our numerical experiments show that the method is very promising, at least for ...

The book also addresses linear programming duality theory and its use in algorithm design as well as the Dual Simplex Method, Dantzig-Wolfe decomposition, and a primal-dual interior point algorithm.

Ron Shamir, Probabilistic Analysis in Linear Programming, Statistical Science, Vol. 8, No. 1, Report from the Committee on Applied and Theoretical Statistics of the National Research Council on ...

About the same time, he invented the “simplex method,” an algorithm for solving linear programming problems.