qp() in Octave 3.0.0 returns result egregiously violating input constraints

[Ben Abbott]

On Apr 6, 2008, at 1:29 PM, Gabriele Pannocchia wrote:
> Hi,
>
> I ran the example and got a result that is feasible with respect to
> equality constraits:
> octave:8> norm(A*X-B)
> ans =  2.5177e-15
> octave:19> tol = 10*eps; all(A_IN*X < A_UB + tol) & all(A_IN*X >  
> A_LB -
> tol)
> ans =  1
> octave:20> tol = 10*eps; all(X < UB + tol) & all(X > LB - tol)
> ans =  1
>
> However, the solver did not converge as it reached the maximum  
> number of
> iterations:
> INFO =
> {
>  solveiter =  200
>  info =  3
> }
>
> One reason for not reaching convergence could be the fact that the
> Hessian of the objective function is NOT positive definite (it  
> actually
> INDEFINITE because it has at least a negative eigenvalue):
> octave:23> min(eig(H))
> ans = -0.0011912
>
> Even the projected Hessian is not positive definite (we can say that  
> it
> is semi-definite):
> octave:26> Z = null(A);min(eig(Z'*H*Z))
> ans = -5.0136e-122
>
>> octave:7> result = X'*H*X + X'*Q
>> result =  5.0743e-06
>
> You can see the objective function in the variable OBJ, and please
> notice that it is: 0.5*X'*H*X + X'*Q
> octave:25> OBJ
> OBJ =  2.5372e-06
>
> There is no guarantee that qp converges for non convex QPs, and indeed
> convergence of indefinite (or semi-definite) programs is a large topic
> in optimization.
>
> Cheers,
> 	Gabriele

Thanks Gabriel,

Might it make sense to add a check to qp and warn in the event the  
problem is non-convex?

If so, what would be appropriate?

Ben