simplex method

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 ?
Again, we solve this problem with the Simplex method.
Gale (1969) recommended to use for inequalities the lexicographic variant of the simplex method of Dantzig et al.
As the step of the simplex method shrinks gradually when a local optimum is found, the simplex method may also become trapped in a local optimum.
The idea is to transform a problem with fuzzy parameters to a crisp version in the LPP form and to solve it by the simplex method.
The reader would be benefited if the introduction of a constraint in sensitivity analysis is also explained with the help of dual simplex method.
The second edition includes the new MATLAB anonymous functions, new coverage of rational function interpolation, replacement of Brent's method of root finding with Ridder's method, and replacement of Fletcher-Reeves method of optimization with the downhill simplex method.
This scheme thus avoids the use of the simplex method.
With examples illustrating nearly every topic, the authors introduce linear programming with a graphical example, explain the simplex method, and show how to perform duality and sensitivity analysis.
2] The mediation operator helps to deduct the medium value of the vector c depending on the weighting of each feeding source selection; figure (3) shows the constraints intervals of the optimal model, resulted from simplex method approach.
We use in this work only the DHCIAC track algorithm, that uses the method of the ant colony [10] for global search, and the dynamic simplex method [32] for local search.
However, the simplex method requires the variables to be non-negative, that is, it requires the polyhedron to be within the positive domain.
disp_sma1 is a program to obtain the optimum underground velocity structure for a given dispersion curve of Rayleigh waves based on the Downhill simplex method combined with the simulated annealing approach.