% QP with H close to -I on unit box; min at every corner of the box
clear;

% number of variables
n = 10;

% form a random  symmetric matrix (may be indefinite)
H = rand(n,n); H = H + H';
H = -eye(n) + 0.1*H;
f = zeros(n,1);

% null inequalities
A = zeros(1,n); b = 0;

% null equality constraints;
Aeq = []; beq = [];

% unit bounds
lb = -ones(1,n); ub =  ones(1,n);

options = optimset('LargeScale','off');

K = 5;
% solve K times, starting from a (different) random vector each time,
% storing the results in xsol
xsol = zeros(n,K);
fsol =zeros(1,K);

for i=1:K,
   x = 2*(rand(n,1)-.5);
%   x= .99 + .01*rand(n,1);
  [x,fval,exitflag, output, lambda] = quadprog(H,f,A,b,Aeq,beq,lb, ...
					       ub,x,options);
  xsol(:,i) = x;
  fsol(1,i) = fval;
end

% print solution array
xsol
fsol