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

[Olaf Till]

Follow-up Comment #14, bug #47314 (project octave):

Adding Rays comment here (replying per E-Mail does not reach the bug tracker
...):

On Mon, Mar 28, 2016 at 11:27:43AM -0400, Ray Zimmerman wrote:
> I just posted the results from Matlab.
> 
> Another “justification” for the convention chosen by Matlab (and
numerous other solvers, such as Octave’s own LP solver, GLPK) is that a
positive shadow price on an inequality corresponds to the sensitivity of the
objective to relaxing the constraint (i.e. to an increase in b for the
standard A*x <= b formulation). Similarly, for an inequality constraint, it is
the sensitivity of the objective function to an increase in the righthand side
of the equality constraint A * x  = b.
> 
> I hadn’t thought about the fact that tight variable bounds might be
translated into an equality constraint. But it is true, that in such cases,
you’ll need to be careful to apply the absolute value of the lambda to the
correct bound.
> 
> Thanks,
> 
>    Ray

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