Thread Subject:

quadprog

Hello,
I'm using quadprog function for solving quadratic problrm with equality constraint matrix wich is not full rank matrix.
Would you please let me know if my problem can be solved by MATLAB? If not Is there any way that I can use for solving this problem with matlab please?
Thank you very much.
~M

On 12 Apr., 06:03, "Mati " <matoo...@yahoo.com> wrote:
> Hello,
> I'm using quadprog function for solving quadratic problrm with equality constraint matrix wich is not full rank matrix.
> Would you please let me know if my problem can be solved by MATLAB? If not Is there any way that I can use for solving this problem with matlab please?
> Thank you very much.
> ~M

QUADPROG can be used within MATLAB if you have access to the
optimization toolbox.
Take a look at
http://www.mathworks.de/help/toolbox/optim/ug/quadprog.html
Or do you search for alternatives because you don't have this toolbox
available ?

Best wishes
Torsten.

"Mati " <matooloo@yahoo.com> wrote in message <jm5k66$7vo$1@newscl01ah.mathworks.com>...
> Hello,
> I'm using quadprog function for solving quadratic problrm with equality constraint matrix wich is not full rank matrix.
> Would you please let me know if my problem can be solved by MATLAB? If not Is there any way that I can use for solving this problem with matlab please?
> Thank you very much.

As Torsten says, quadprog is part of the optimization toolbox.

To the extent that it is part of MATLAB, then yes, you can
solve it with MATLAB. Or, you could write such a tool yourself.

But, no, without your understanding how to solve such a
problem yourself, you cannot directly solve a quadratic
programming problem under equality constraints.

Could you convert a QP problem into one that a tool like LSE
from the file exchange could solve? Yes, if you really have no
more than a QP on a positive semi-definite matrix subject to
equality constraints. A matrix square root (sqrtm or chol)
would be needed.

I'll let someone else guide you through this however. Or, they
can teach you how to solve the resulting LSE problem itself.
Easier is just to use quadprog, since you have it.

John

"Mati " <matooloo@yahoo.com> wrote in message <jm5k66$7vo$1@newscl01ah.mathworks.com>...
> Hello,
> I'm using quadprog function for solving quadratic problrm with equality constraint matrix wich is not full rank matrix.
====================

I don't see why QUADPROG would fail when Aeq is not full rank, as long as the constraints do indeed have a feasible solution within TolCon. But I'm jut guessing, really...

What is the dimension of your problem. Would it be such a big deal to weed out the redundant data from Aeq until it becomes full rank?

"Matt J" wrote in message <jm68kc$g5i$1@newscl01ah.mathworks.com>...
> "Mati " <matooloo@yahoo.com> wrote in message <jm5k66$7vo$1@newscl01ah.mathworks.com>...
> > Hello,
> > I'm using quadprog function for solving quadratic problrm with equality constraint matrix wich is not full rank matrix.
> ====================
>
> I don't see why QUADPROG would fail when Aeq is not full rank, as long as the constraints do indeed have a feasible solution within TolCon. But I'm jut guessing, really...
>
> What is the dimension of your problem. Would it be such a big deal to weed out the redundant data from Aeq until it becomes full rank?



And if Aeq has full row rank, but not full column rank, you're definitely fine.

"Matt J" wrote in message <jm68kc$g5i$1@newscl01ah.mathworks.com>...
> "Mati " <matooloo@yahoo.com> wrote in message <jm5k66$7vo$1@newscl01ah.mathworks.com>...
> > Hello,
> > I'm using quadprog function for solving quadratic problrm with equality constraint matrix wich is not full rank matrix.
> ====================
>
> I don't see why QUADPROG would fail when Aeq is not full rank, as long as the constraints do indeed have a feasible solution within TolCon. But I'm jut guessing, really...
>
> What is the dimension of your problem. Would it be such a big deal to weed out the redundant data from Aeq until it becomes full rank?

I don't know that quadprog HAS failed. That was not at all
stated. We have no idea as to why the OP does not want
to use quadprog, and without more information, there is
no way to answer the question.

John

On Apr 12, 8:04 am, "John D'Errico" <woodch...@rochester.rr.com>
wrote:
> "Matt J" wrote in message <jm68kc$g5...@newscl01ah.mathworks.com>...
> > "Mati " <matoo...@yahoo.com> wrote in message <jm5k66$7v...@newscl01ah.mathworks.com>...
> > > Hello,
> > > I'm using quadprog function for solving quadratic problrm with equality constraint matrix wich is not full rank matrix.
> > ====================
>
> > I don't see why QUADPROG would fail when Aeq is not full rank, as long as the constraints do indeed have a feasible solution within TolCon. But I'm jut guessing, really...
>
> > What is the dimension of your problem. Would it be such a big deal to weed out the redundant data from Aeq until it becomes full rank?
>
> I don't know that quadprog HAS failed. That was not at all
> stated. We have no idea as to why the OP does not want
> to use quadprog, and without more information, there is
> no way to answer the question.


I don't know that quadprog _has_ failed either, but it seems pretty
clear that the OP is concerned that it might fail if a non-full rank
Aeq is given to it. Otherwise, why mention that detail?

Thank you very much.
my constraint Matrix dimention is 50*70 and the problem is that the matrix is not full rank because columns are dependent.
If rows are dependent MATLAB just consider the independent roes for solving the problem but in the case that column are dependent I don't know what would be MATLAB approach.
my matrix has some columns with 0, 1, -1 value that makes it to be not full rank.
Thank you very much.
 

"Matt J" wrote in message <jm69gg$il4$1@newscl01ah.mathworks.com>...
> "Matt J" wrote in message <jm68kc$g5i$1@newscl01ah.mathworks.com>...
> > "Mati " <matooloo@yahoo.com> wrote in message <jm5k66$7vo$1@newscl01ah.mathworks.com>...
> > > Hello,
> > > I'm using quadprog function for solving quadratic problrm with equality constraint matrix wich is not full rank matrix.
> > ====================
> >
> > I don't see why QUADPROG would fail when Aeq is not full rank, as long as the constraints do indeed have a feasible solution within TolCon. But I'm jut guessing, really...
> >
> > What is the dimension of your problem. Would it be such a big deal to weed out the redundant data from Aeq until it becomes full rank?
>
>
>
> And if Aeq has full row rank, but not full column rank, you're definitely fine.

"Mati " <matooloo@yahoo.com> wrote in message <jm9d5r$he6$1@newscl01ah.mathworks.com>...
> Thank you very much.
> my constraint Matrix dimention is 50*70 and the problem is that the matrix is not full rank because columns are dependent.
> If rows are dependent MATLAB just consider the independent roes for solving the problem but in the case that column are dependent I don't know what would be MATLAB approach.
=================

Mati,

Dependent columns are the normal case. If you had linearly independent columns, there could be at most one solution to the equality constraints and the problem would be trivial.

Dependent rows are the more problematic situation. I agree that if the augmented matrix [Aeq,beq] contains dependent rows, the redundant rows will likely be ignored. However, the same can't be said if the rows of Aeq alone are dependent. For example, the following problem data has Aeq with dependent rows, but quadprog will see the problem as infeasible if you use the default value for the TolCon tolerance parameter setting.

Aeq=ones(2,3)
beq=[1;1.0001]