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

[AsmaA]

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
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].

> 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)
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?
For other examples (now uncommented in runquadprog.m) lambda.eqlin is
-1 * matlab's values but the multipliers corresponding to the lower
bounds and the ordering is fine.

Kind Regards,
Asma.

[1] https://github.com/AsmaAfzal/octave_workspace/blob/master/quadprog.m
[2] https://github.com/AsmaAfzal/octave_workspace/blob/master/runquadprog.m

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