Questions tagged [extreme-rays]

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6
votes
1answer
89 views

Extreme rays of a small polyhedral cone: How do I get them?

In a nutshell I have a small 2-dimensional polyhedral cone. $$C=\{(x_1,x_2): 2x_1-x_2 \leq 0, x_1+3x_2 \leq 0\}$$ I am looking for a simple, illustrative, procedure to get its extreme rays. Any ...
5
votes
1answer
86 views

Find Extreme direction of equality constraints

I think this is a very basic question, but I failed to find an algorithm for this... When I have a set of inequality constraints, $Ax \leq b$ as my feasible region, I can set $b = 0$ and find $n-1$ ...
6
votes
1answer
212 views

Extreme point and extreme ray of a network flow problem

"It is a well-known result in network flow theory that an extreme point and an extreme ray of the polyhedron defined by the convex hull of feasible region corresponds to a path and cycle (resp.) ...
3
votes
2answers
229 views

How to get an extreme ray of an LP from Gurobi

I am working on a problem of form \begin{equation} \begin{array}{l @{\quad} l} \mathrm{max}_{x, u} & p^{\top} u \\ \text{st.} & A u + a x \leq 0 \\ & x \in \{0, 1\...
9
votes
1answer
147 views

Extreme rays in polymake

I am trying to find extreme rays of a polyhedral cone using polymake. My understanding is that in a cone, every feasible solution is also a ray and an extreme ray is a ray that cannot be written as ...
12
votes
2answers
542 views

Generating all extreme rays

I am trying to understand a problem and would like to generate all extreme rays for a given set of linear constraints. With the Python interface of CPLEX, I was able to generate a single ray (not sure ...