karmarkar

Scilab Function
Last update : 12/01/2004

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);