/* Problem Setup */
/* linear vector in consumer surplus */
a={14.252,33.119};
/* quadratic matrix in consumer surplus */
aa={-0.00478 -0.00796,
    -0.00796 -0.02590};
/*  linear vector in producer surplus */
b={-4.780,-15.140};
/* quadratic matrix in producer surplus */
bb={0.007097 0.001577,
    0.001577 0.025684};
/* constraint matrix */
ac={1 0 -1 0,0 1 0 -1};
/* nullspace of constraint matrix */
z=null(ac);
/* candidate point for optimum */
xstar={1000,750,1000,750};

/* objective function value */
f=(a|-b)'xstar+.5*xstar'((aa~zeros(2,2))|(zeros(2,2)~-bb))*xstar;
/* gradient vector value */
g=(a|-b)+((aa~zeros(2,2))|(zeros(2,2)~-bb))*xstar;
/* compute the projected gradient */
projg=g'z;
projg;
/* norm of the projected gradient */
norm=sqrt((g'z)*(g'z)');
norm;
/* projected Hessian matrix */
hessp=z'((aa~zeros(2,2))|(zeros(2,2)~-bb))*z;
/* eigenvalues of the projected Hessian matrix */
{va,ve}=eigrs2(hessp);
va;