theta=33;
R=[cos(theta),-sin(theta);sin(theta),cos(theta)];
R1=R'

function [f,g,ind]=cost(x,ind) 
  f=1/2* (R*x+1)'*(R*x+1) 
  g = R'*R*x +R'*[1;1]
endfunction

[f,xopt]=optim(cost,[5;5])

// fixons une contrainte 
// R1* x >=0 

function [f,g,ind]=cost1(x,ind) 
  f=1/2* (R*x+1)'*(R*x+1) + lambda'*R1*x 
  g = R'*R*x +R'*[1;1] + (lambda'*R1)'
endfunction

// Itérations 

lambda = [0;0]; 
xopt=[5;5]
rho=0.2
//res=[]
for i=1:100
  [f,xopt]=optim(cost1,xopt)
  lambda =max( lambda + rho*R1*xopt,0)
  //res=[res,xopt]
end