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by Abbas Omidi
05 Nov 2021, 20:13
Forum: General Discussion
Topic: Finding integer vertices in an MILP
Replies: 4
Views: 230

Re: Finding integer vertices in an MILP

Dear Dr. Paffenholz, Many thanks for your comments. Actually, I mean by extreme points is integer vertices (integer convex hull) and the provided output of the function is what exactly I was looking for. But the thing that was strange is, I could not get the results from the mentioned function last ...
by Abbas Omidi
05 Nov 2021, 11:43
Forum: General Discussion
Topic: Finding integer vertices in an MILP
Replies: 4
Views: 230

Re: Finding integer vertices in an MILP

Dear Dr. Paffenholz, Many thanks for your prompt reply. I am aware of, the finding all of the integer vertices of a MILP problem needs to consume a lot of time and effort, but for a trivial problem, it is very helpful for understanding the problem structure. W.r.t the above problem, As it has four v...
by Abbas Omidi
03 Nov 2021, 12:32
Forum: General Discussion
Topic: Finding integer vertices in an MILP
Replies: 4
Views: 230

Finding integer vertices in an MILP

Dear support team, I am trying to implement a decomposition algorithm and I have to work with extreme points of the MILP. As I asked some questions about defining polyhedron, I have tried to use the same approach to find integer vertices, but I am failing to do that. Also, I am working on lattice an...
by Abbas Omidi
02 Oct 2021, 10:09
Forum: General Discussion
Topic: how to define integer polytope by matrix representation
Replies: 6
Views: 589

Re: how to define integer polytope by matrix representation

Dear Thomas, Many thanks for your clarifying where I was doing wrong. It now makes sense as the two different methods (matrix & in/eq form) could produce the same solution. Would you say places, where I can find the related documents about what Dr. Joswig mentioned for the polyhedron specifications?...
by Abbas Omidi
28 Sep 2021, 11:44
Forum: General Discussion
Topic: how to define integer polytope by matrix representation
Replies: 6
Views: 589

Re: how to define integer polytope by matrix representation

Dear Prof. Joswig, Many thanks for your detailed explanation. As I am pretty new in this field, what you answered is very interesting to me. Would you say please, how we can find the related documents about the interpretation of the vertices method? I mean, how can I find the number of vertices, ray...
by Abbas Omidi
28 Sep 2021, 09:22
Forum: General Discussion
Topic: how to define integer polytope by matrix representation
Replies: 6
Views: 589

Re: how to define integer polytope by matrix representation

Dear support team, Thanks for your helpful answer. I have tried this and works well, but I have an issue with calculating the vertices by defining the polyhedron based on both methods. Let's say, in the first attempt, I define the problem by the following method: // $p = new Polytope(INEQUALITIES=>[...
by Abbas Omidi
26 Sep 2021, 13:25
Forum: General Discussion
Topic: how to define integer polytope by matrix representation
Replies: 6
Views: 589

how to define integer polytope by matrix representation

Dear support team, First, thanks for your useful tool. I am trying to define a polyhedron (actually, integer polytope) by using "https://shell.polymake.org/". I would like to represent the polyhedron of the GAP (generalized assignment problem) that is defined by the following constraints: // CPLEX l...

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