Re: Slow performance on "Select minimum" task

Dear Kevin,

Yes, it is indeed a matrix of floats.

Thanks for the quick replies and your help though :)

Best,
Jan

2018-05-29 15:45 GMT-04:00 Kevin Martin <[email protected]>:

>
> > On 29 May 2018, at 16:32, Jan van Rijn <[email protected]> wrote:
> >
> > It is true that I introduced a binary variable per matrix element, and
> it would be great if we could get rid of it.
> > From your formulation, I struggle to understand the last statement:
> > What exactly does M(j, i) represent?
>
> I have re-read your problem and I may have misinterpreted it. I thought
> your matrix was binary, as in each element was in {0,1}, the sum condition
> was supposed to be i:M(j,i)=0, which would be the sum of all the row
> inclusion (x_j) variables where the Matrix element for the column was 0.
> The idea being that if none of the rows corresponding to a are 0 selected,
> the minimum of the column must be 1.
>
> As I re-read your original email, I now think that each element may be
> fractional somewhere in the closed interval [0,1]. If this is the case, I
> think the problem may be quite hard, for general M, I can’t think of an
> obvious way to formulate it better.
>
> I guess the best approach depends on your requirements. If you are just
> after something ok and quick that scales, I would start with a convex
> approximation of the column minimum, formulate a convex problem based on
> this, and use something like Ipopt to solve it, round the result. If
> instead, you want something within known bounds of optimal you can try
> adjusting the glpk termination criteria (I think by default it tries to
> prove optimality) or maybe provide some heuristics to help prune the search
> space, see GLP_IHEUR in the glpk manual.
>
> Thanks,
> Kev
>
>
>

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