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

[Gabriele Pannocchia]

Hi Josh

> My mistake, The l2-norm of eVrH is 1.  I didn't realize Z was a matrix
> and so was printing too many entries of eVrH.

Yes, Z is a matrix. Briefly (to avoid bothering people in this list with
linear algebra lectures...), the active set QP solver works in this way:
- the current active set includes ALL equality constraints plus the
inequality constraints that are currently active, i.e. such that the
inequality is actually an equality: we include these constraints in the
active set matrix, denoted by
- Z is computed as a basis for the null-space of Aact, i.e. it is a full
rank matrix such that Aact*Z = 0. In the __qp__.cc Z is computed with a
static function (at the beginning of the code) which replacates what it
is done by null.m. It is based on an SVD, so even each column of Z
should have l2-norm equal to 1.
- The step is computed (when info=1) as: Z*eVrH.

Can you confirm that the columns of Z have unitary norm?

If you compute a very small step p, you should have 
(max_p < rtol) = true in line 304. Can you confirm?

Gabriele

> It's a bit hard tracking down this bug because I don't have a good
> idea of the math behind the code so don't know what to expect.

I understand and the other problem is that I cannot reproduce the error
on my linux-i686 machine.
If you can, and want to understand how the code works, please have a
look at Chapter 16 of Nocedal and Wright "Numerical Optimization",
Springer-Verlag 1999. In particular, the basic algorithm is described in
section 16.4.

Cheers,
	Gabriele