[Help-glpk] Enumerating the vertex neighborhood

[Olivier Liess]

[please excuse me if this subject was  already discussed, I found 
nothing about this in the archive]

Because of convexity issues in the problem I'm currently studying, I 
want to obtain the neighbors of the optimal vertice. The easiest way for 
this is to start from the simplex tableau corresponding to the optimal 
solution, and make a pivot operation with each non-basis [auxiliary or 
stuctural] variable, one after the other.

I was thinking of using lpx_eval_tab_{row,col} with 
lpx_{prim,dual}_ratio_test to be given the variable leaving the basis 
when the selected non-basic variable is forced to enter. But I couldn't 
manage to "fix" this state and get the new values (of course, values are 
not automatically recomputed when operations are done on the basis, and 
lpx_simplex juste gives me the same optimal value).

So, is there a way to fix the status of a variable ? Or force a pivot 
operation on a given variable ?

Bonus question : what is the meaning of the "how" argument in the 
lpx_{prim,dual}_ratio_test functions ? My limited kowledge in this area 
tells me that, on entering or leaving the basis, a variable has a 
deterministic behaviour.  therefore I don't see what is the use of this 
parameter.

Well, time to wait for the answer(s) :)

Thanks Andrew for this great tool, and to everyone else for beeing so 
active on this project

Olivier Liess
Universite d'Avignon et des Pays de Vaucluse
France