On 2013-08-16 11:48, Michael Hennebry wrote:
On Thu, 15 Aug 2013, sgerber wrote:
Is it possible to enumerate the neighboring feasible solutions of
the solution of an lp?
I assume that in order to decide if the simplex algorithm can stop
it is necessary to check all neighboring feasible solutions. Is this
right? And if so is there a way of enumerating the neighborhood of
feasible solutions around the optimal one?
The simplex algorithm does not check all neighboring vertices.
It checks all extreme rays of a cone that includes the feasible
region.
The number of rays is the dimension of the problem.
Allowing for degeneracy, the number of adjacent vertices
can be much larger than the dimension of the problem.
Thank you for your answer.
There is no degeneracies in my problems. I assume the cone you are
describing is the intersection of the half spaces of the active
constraints.
Also how does degeneracy increase the number of neighbors? Note,I ask
for the neighbors of a single optimal solution, i.e. a single vertex,
not the neighbors of all vertices with optimal solution.
My question still stands is it possible to enumerate the neighbors of a
vertex with gplk?
-Sam
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