Re: RFC: quadprog/lsqlin with __qp__ (Re: GSoC 2015, optim)

[Olaf Till]

On Mon, Jul 13, 2015 at 07:40:47PM -0700, AsmaA wrote:
> Hi Olaf,
> 
> Thank you for your reply.
> 
> > But currently it is accepted if one of A and b is empty and the other
> > not. What's the sense in this?
> 
> Are you referring to qp.m (lines 253 onward)? qp.m gives an error if

I'm refering to your code of quadprog.m.

> A_in is empty but it works if A_in is given and A_ub is empty.
> Example:
> 
> qp ([],H,f,Aeq,beq,lb,ub,[],A,[])
> 
> This works. qp simply ignores inequality constraints due to if checks
> in lines (258, 266, 275)
> Matlab gives an error if A is empty and b is not and vice versa. Example:
> 
> quadprog (H, f, A, [], Aeq, beq, lb, ub)
> 
> Error: The number of rows in A must be the same as the length of b.
> 
> I have added this check in line 181 of quadprog. Please refer to the
> updated code [1].

The updated code still accepts (H, f, A, [], ...) and (H, f, [], A, ...).

> 
> > Running the example which is not commented out, I get
> >
> > ...
> > lb = -0.1*ones(4,1);
> > ...
> > [x,obj,flag,op,lambda]=quadprog(C'*C,-C'*d,A,b,Aeq,beq,lb,ub)
> > x =
> >
> >   -0.10000
> >   -0.10000
> >    0.15991
> >    0.40896
> > ...
> > lambda =
> >
> >   scalar structure containing the fields:
> >
> >     lower =
> >
> >        0.06743
> >        0.00000
> >        0.24993
> >        0.00000
> > ...
> >
> > which indicates an error in the ordering of lambda for lower bounds.
> 
> The values are different from Matlab's, but I was more concerned about
> arranging multipliers from qp in the right order. Running this example
> with qp I get:
> 
> [x, obj_qp, INFO, lambda]  = qp ([], C'*C,-C'*d,Aeq,beq,lb,ub,[],A,b)
> 
> lambda =
> 
>    0.01654
>    0.06743
>    0.00000
>    0.24993
>    0.00000
>    0.00000
>    0.00000
>    0.00000
>    0.00000
>    0.00000
>    0.49819
>    0.00000
> 
>  I am not sure why the values are swapped (third and fourth values)

I'd rather say the 2nd and 3rd values are swapped.

> and the sign is different for lambda.eqlin.
>  lambda.eqlin in matlab is -0.0165 for this example and lambda.lower =
>     0.0674
>     0.2499
>          0
>          0
> 
> Can you explain why this is so?

I don't think I've currently the time to dig into __qp__.cc to explain
the swapping. But it's an indication that nobody ever used the lambda
returned by __qp__.cc.

To repeat myself, I'd appreciate if someone could tell me what the
user can do with that lambda.

Olaf

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