[Octave-bug-tracker] [bug #47314] optim package: quadprog() equality constraints have opposite sign

[Olaf Till]

Follow-up Comment #12, bug #47314 (project octave):

Forgot to paste 'A' in last example, it was A = [-3, 5];. Also, the second
call to quadprog should be with '-A', and in the output 'lambda2' (which has
opposite sign).

Thinking further about what is in the last post, this argument for Octaves
variant of lambda seems quite strong, reformulated:

- quadprog specifies, in the doc, Aeq * x = b for equality constraints (not
the -- equivalent -- -Aeq * x = -b).

- the usual definition of lambda in equality constraints is that it satisfies
the equation ('H' and 'f' as used by the doc): '.5Hx + f =
transpose_of_given_constraint_matrix * lambda' (It seems not usual to negate
the given constraint matrix, and formally it would be an unnecessary
additional step.)

- so someone using lambda should expect (if he doesn't check it) that the
matrix is not (implicitely) negated for the returned gamma -- should expect
what Octaves quadprog does, not Matlabs.

So I'm in favour of keeping our quadprog's current behaviour, but I still hope
for some input.


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