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Affine Scaling

This a method due to Vanderbei e.a. in the 1980s.

function affinescaling (A:real, b:real column, c: real vector,

   Minimize c.x with A.x=b using an inner method
  
   The method used it due to Vanderbei e.a. It takes the current
   solution x to (1,...,1) and uses a direction c projected to the
   kernel of A.
  
   The start vector x must be an inner vector. If it is missing, an
   additional variable is used, and A is expanded such that
   x=(1,...,1) is a feasible start point.
  
   A : mxn matrix
   b : 1xm column vector
   c : nx1 row vector
   gamma : 0<gamma<1 (optional)
   x : 1xn start vector (optional)
  
   Returns : xopt (1xn) vector
  
   history : If true {xopt,X} is returned, where X contains all points
   visited.

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