Re: [Bug-glpk] glp_warm_up

[Andrew Makhorin]

> > On Thu, 2013-03-07 at 18:25 -0600, David T. Price wrote:
> > > I will look for it soon. The same bug occurs in check_kkt as well. Did 
> > > you fix it there?
> > 
> 
> 
> I fixed the similar bug in lpx_check_kkt. Please see a patched version
> of glpapi10.c attached. You need to replace that file and rebuild the
> package as usual. (The patch is for v.4.48.)
> 

The bug in lpx_check_kkt was fixed incorrectly. Please DO NOT USE the
patch.

> > I don't understand your argument. Consider the problem:
> > 
> > Maximize 5 * x1
> > 
> > Bounds
> > 1 <= x1 <= x2.
> > 
> > The trivial basis will put x1 on the boundary nearer 0, namely x1 = 1. 
> > This is clearly primal feasible. However, the optimal solution of the 
> > problem is x1 = 2. So the starting solution can't be dual feasible. 
> > However, glp_warm_up says that the starting solution is "dual feasible" 
> > and hence the status reported is "optimal". That is wrong.

In this case the complementary slackness condition is violated, neither
primal nor dual feasibility conditions checked by lpx_check_kkt.

This condition is usually not checked for basic solutions, where it is
satisfied automatically (unlike interior-point solutions). However, this
is so until double-bounded variables appear.