Re: [Help-glpk] Two capabilities questions

[Andrew Makhorin]

>1) Can GLPK solve problems where the solution vector has bounded but
>   negative coefficients? The problem I am interested in solving has
>   coefficients in the range [-1.0, 1.0]. (I am aware that I can fiddle
>   the problem to require coefficients >= 0 but this further complicates
>   matters).

If you mean bounds of structural variables, they can be of any sign.
So, you can set bounds that you need using API like follows:

   glp_set_col_bnds(lp, j, 'D', -1.0, +1.0);

or specify them in MPS file in a usual way. For details see "GLPK User's
Guide" included in the distribution.

>2) Is is possible to feed a known but sub-optimal initial feasible
>   solution into GLPK and have it optimise that? The problem I am
>   working on has very tight constraints and many LP solvers have
>   trouble finding an initial feasible solution.
>
>3) Following on from 2), what about an initial solution which is close
>   to being in the feasible set but isn't.

You can use API routines glp_simplex1() and glp_simplex2(), which allow
you to solve LP using an initial basis explicitly specified in LPI. For
details see the text file 'newapi.txt' included in the package.