# 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.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.

## 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 ?
Then a simplex algorithm has been proposed to solve such N LP-problems.
The Nelder-Mead algorithm (NM) called also simplex algorithm has been suggested by Spendley, Himsworth, and Hext in 1962.
Megiddo, "A simplex algorithm whose average number of steps is bounded between two quadratic functions of the smaller dimension," Journal of the ACM, vol.
The optimization method presented in this paper is based on the Nelder-Mead simplex algorithm to improve torque capacity estimation for the K0 clutch (disconnect clutch) control feature applied to hybrid automatic transmissions.
Nelder-Mead Simplex Algorithm was proposed in 60's and it had been enormously popular direct search method for unconstrained minimization.
A hybrid intelligent algorithm that consists of a network simplex algorithm, a simulation, and a genetic algorithm was developed to solve the stochastic and fuzzy models above.
Several iterative algorithms, which consist in generating a sequence of testing and updating of a trial solution based on a linear least-squares algorithm, were applied to obtain the optimal source locations coordinates: grid search, simplex algorithm, Geiger's method [10],...
It begins with an approach to problem formulation, then describes geometric motivation, linear algebra and algebraic steps related to the simplex algorithm, standard phase 1 problems, and computational implementation of the simplex algorithm.
The simplex algorithm [15] is the classical method for solving linear programs.
[28] proposed a gray-encoded hybrid accelerating genetic algorithm (GHAGA) with Nelder-Mead simplex searching operator and simplex algorithm for the global optimization of dynamical systems.
Like the simplex algorithm, the NNLS algorithm by Kong (2007) has a basis B consisting of a set of linearly independent columns of E used for solving a system of equations.

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