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## Re: R: [Help-glpk] Multiobjective problem

**From**: |
Andrew Makhorin |

**Subject**: |
Re: R: [Help-glpk] Multiobjective problem |

**Date**: |
Fri, 28 Aug 2009 16:10:33 +0400 |

>*> If the current basic solution is optimal and you free some previously*
>*> fixed variables, the solution cannot become primal infeasible; it may*
>*> become only non-optimal (dual infeasible). Or I misunderstand*
>*> something?*
>* In my experience the solution becomes primal infeasible.*
>* Let's think to an extreme case: if you fix all the variables to their*
>* optimal value, all the columns will have the basis status GLP_NS (non-basic*
>* fixed variable). But when you free all the variables, the columns will stay*
>* out of basis: the basis status will be updated to GLP_NF, or GLP_NU, or*
>* GLP_NL depending on the new bounds. In my case, I set only the lower bound*
>* to 0, so that in the current solution all the variables have 0 as value*
>* (status GLP_NL), which corresponds to a primal infeasible solution.*
>* I'm wrong?*
No, you are right. (I meant relaxing bounds of basic variables.)
To perform re-optimization you may try to use the dual simplex (with
the lp presolver disabled), because if the current basic solution is
optimal, it remains dual feasible after changing bounds of variables.