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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