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

[Joshua Redstone]

Hi Gabriele,
So the input matrix H is actually a covariance matrix - with some missing
values.  I'm under the impression that a standard approach is to fill in the
values by doing a maximum likelihood estimation assuming the random vars are
joint-normally distributed, but I didn't want to make that assumption, and
so the matrix isn't quite consistent - i.e., the variance can be slightly
negative for a linear combination of random vars as indicated by H (i.e.,
x'*H*x can be slightly < 0).

As for debugging the intel osx octave problem, I'm still working on
compiling octave on my intel mac... :).
Josh

On Sun, Apr 6, 2008 at 10:29 AM, Gabriele Pannocchia <
g.pannocchia at ing.unipi.it> 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
>
>
-------------- next part --------------
An HTML attachment was scrubbed...
URL: https://www.cae.wisc.edu/pipermail/bug-octave/attachments/20080406/83b775a3/attachment.html