Re: help in modifying __qp__.cc

[Gabriele Pannocchia]

Actually, it is not that simple. If we have a feasible region described
by:
   Ain*x <= bin
we cannot tell if the constraints are redundant by just looking at the
rank of Ain. 

Consider the simple case of box constraints on a scalar variable:
       -1 <= x <= 1
The constraint matrix is Ain=[1;-1]  (and bin=[1;1])
Clearly Ain has one redundant row, but the two constraints cannot be
active at the same time. Thus we should keep them both or we would
modify the feasible region.

If one wants to remove redundant constraints then one has to solve "nin"
LPs (where "nin" is the number of rows of Ain). This preprocessing in
most cases would take more time then solving the QP itself.

Gabriele
> It's been awhile since I wrote my own interior point method QP code  
> (not ready for prime-time), but is there a reason not to use an  
> economy size rank revealing QR decomposition [q,r,p] = qr(A,1) at  
> start to reduce the dimension of the constraints if they are or can be  
> redundant?  The flop cost would be less than one iteration of a QP  
> iterative method.
> 
> A. Scottedward Hodel address@hidden
> http://homepage.mac.com/hodelas/tar
> 
> 
> 
>