# simplex method

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## simplex method

[′sim‚pleks ¦meth·əd]
(mathematics)
A finite iterative algorithm used in linear programming whereby successive solutions are obtained and tested for optimality.

## simplex method

(algorithm)
An algorithm for solving the classical linear programming problem; developed by George B. Dantzig in 1947.

The simplex method is an iterative procedure, solving a system of linear equations in each of its steps, and stopping when either the optimum is reached, or the solution proves infeasible. The basic method remained pretty much the same over the years, though there were many refinements targeted at improving performance (eg. using sparse matrix techniques), numerical accuracy and stability, as well as solving special classes of problems, such as mixed-integer programming.
References in periodicals archive ?
Downhill Simplex methods were better able to find the global optimum with an average of 10 percent with the larger number of performed simulation experiments--see Error
Other developments included the beginnings of the development of nonlinear optimization, the application of linear optimization methods to management theory in 1951, the publication of the first linear optimization textbook in 1953, the development of dual simplex methods in 1953, and early methods for transportation problems in 1954 (Brentjes, 1994).
To solve a linear programming problem, Solver operates directly on the Jacobian matrix using a straightforward implementation of the simplex method with bounded variables to determine the optimal solution.
The stopping conditions for GRG2 are the same as those for the simplex method.
For integer programming problems, Solver uses a branch-and-bound algorithm that can use either the simplex method or GRG2 to solve its subproblems.
Also, we see that average speedups over the DND and simplex methods increase to about 2.
From the solution times plotted in Figures 5, 6, and 7, we conclude that while parallel efficiencies decrease with problem size, the distributed nested-decomposition algorithms, particularly the EDND strategies, provide significantly lower solution times in comparison with the SND and simplex methods.
1990] of the simplex method, such a hybrid feature allows one to perform the distributed decomposition of a structured problem first as a series of subproblems, and then solving each of them by vectorizing techniques, thereby reducing solution times.
Comparison of DND with the Simplex Method Speedup over Simplex for Problem Simplex Time Serial DND sc205 2063 0.
Since the first publication of the simplex method by Dantzig, there have been many attempts to find better ways to solve LP problems.
He shows in detail how the simplex method can be considered as a method of feasible directions, and he also shows how the latter can be applied to solve linearly constrained non-linear programming problems.
Thus, it applies the simplex method to a restricted problem made up of the columns of the indicated basic variables.

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