karmarkar

karmarkar — karmarkar algorithm

Calling sequence

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

`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

Computes x which minimizes



                        c'*x

under constraints:



                        a*x = b
                        x>=0



// 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);