FF - 2007-06-10 - Simplex Algorithm, created by the North American mathematician George Dantzig in 1947, is a popular technique for numerical solution of the linear programming problem. This implementation deals with problems expressed in standard form, that means: minimization of a linear function respecting a number of constraints (linear), and that all variables are positive.
We could write the problem (in standard form) in a matrix way:
min f(x) Ax = b x >= 0
where f(x) is a linear function R^n -> R and Ax = b is a linear system of m equations (in matrix form) in n variables, representing the constraints.
In the code below I called Fn the function, Cn the coefficients matrix for the constraints, Cb is the b vector.
See also:
http://en.wikipedia.org/wiki/Simplex_algorithm
Code to be replaced using math, part of tcllib