karmarkar - karmarkar algorithm

Calling Sequence

[x1]=karmarkar(a,b,c,x0)

Parameters

• a : matrix (n,p)
• b : n - vector
• c : p - vector
• x0 : initial vector
• eps : threshold (default value : 1.d-5)
• gamma : descent step 0<gamma<1 , default value : 1/4
• x1 : solution
• crit : value of c'*x1

Description

Computes x which minimizes

                        c'*x
   
    

under constraints:

                        a*x = b
                        x>=0
   
    

Examples

// n=10;p=20;
// a=rand(n,p);c=rand(p,1);x0=abs(rand(p,1));b=a*x0;x1=karmarkar(a,b,c,x0);