%function [F,G] = fun(z)
%function for computing theta and search direction
% z = (nu,mu,u1,u2,u3,u4,psi,x)
function [F,G] = fun(z)
z = z(:);
nu = z(1:4);
mu = z(5:7);
U = [z(8:11) z(12:15) z(16:19) z(20:23)];
x = z(24:25);
psimax = z(26);
sum = 0;
xi0 = 0;
for i = 1:4,
  xi0 = xi0 + nu(i)*(psimax - g(x,U(:,i)));
  sum = sum + nu(i)*gradgx(x,U(:,i));
end %for
xi0 = xi0 - mu(1)*(x(1)*x(2) - 300)...
          - mu(2)*(x(1) - 2*x(2)) ...
          -mu(3)*(0.5*x(2) - x(1));
sum = sum + mu(1)*[x(2);x(1)] + mu(2)*[1;-2] + mu(3)*[-1;0.5];
F = xi0 + 0.5*norm(sum)^2;
%
for i=1:4,
  G(i) = norm(U(:,i))^2 - 1;
end %for
l = ones(7,1);
lambda = [nu;mu];
G(5) = l'*lambda - 1;
G(6) = 1 - l'*lambda;