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simplex method

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simplex method

Standard technique in linear programming for solving an optimization problem, typically one involving a function and several constraints expressed as inequalities. The inequalities define a polygonal region (see polygon), and the solution is typically at one of the vertices. The simplex method is a systematic procedure for testing the vertices as possible solutions.

simplex method [′sim‚pleks ¦meth·əd]
(mathematics)
A finite iterative algorithm used in linear programming whereby successive solutions are obtained and tested for optimality.
(algorithm)simplex method - 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.
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Also included is a previously unpublished technical report from 1980 by Norman Zadeh, who comments on what has yet to be done in the field and gives a simple pivot rule for the simplex method for which it is still unknown if it yields a polynomial time algorithm.
Polyhedral computation by SciTech Book News
The author proposes two optimization algorithms: one based on the SIMPLEX method and a second one that mimics the experimental trial-and-error procedure usually employed in tools manufacture.
Design of optimal extrusion die for a range of different materials by Lebaal, Nadhir; Schmidt, Fabrice; Puissant, Stephan; Schlafli, Daniel / Polymer Engineering and Science
Coupling with Simulation Environment The optimization of utility costs for a billing period is accomplished using the Nelder-Mead simplex method (Nelder and Mead 1965) available in the optimization toolbox of a popular technical computing environment (Matlab 2007).
Optimization of building thermal mass control in the presence of ... by Henze, Gregor P.; Brandemuehl, Michael J.; Felsmann, Clemens; Cheng, Hwakong; Florita, Anthony R.; W / ASHRAE Transactions
 
 
 
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