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Questions tagged [polyhedra]

For questions on the set of points that satisfy a finite set of linear inequalities.

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9
votes
1answer
144 views

Finding the linear functions defining a polyhedron through integer data?

Let's say I have a bunch of linear functions $f_1,\cdots,f_n$ in $k$ variables; then $f_1,\cdots, f_n\le0$ defines a polyhedron $P$ in the $k$-dimensional space. What I'm looking for is going the ...
9
votes
3answers
149 views

Is the “reverse search” algorithm of David Avis the state-of-the-art method for finding discrete solutions to a system of linear inequalities?

Is the "reverse search" algorithm of David Avis the state-of-the-art method for finding discrete solutions to a system of linear inequalities? If it is not, then what is? For $m$ inequalities in $d$ ...
5
votes
0answers
62 views

What are the top three applications (in terms of number of citations) of the “reverse search” algorithm of David Avis?

I can see that this algorithm is quite popular, and that one of the original papers now has 820 citations on Google Scholar. However, what are the most highly cited applications of it? If in Google ...
20
votes
6answers
1k views

How to compare two different formulations of a problem?

I somewhat know how to compare two MILP formulations of a problem that both use the same set of decision variables (as in the classical MTZ vs DFJ formulations of the TSP). I was wondering how two ...
14
votes
2answers
1k views

Polyhedra, Polyhedron, Polytopes and Polygon

About Polyhedra, Polyhedron, Polytopes and Polygon, what do they mean in the context of linear programming and what is the difference between them?
11
votes
1answer
92 views

Simplest way to eliminate redundant constraints due to a new cut

I have a polyhedral set for constraining $x$: \begin{align} \mathcal{P} = \{x \in \mathbb{R}^n_{+} : \ Dx \leq d \} \end{align} where $D \in \mathbb{R}^{m \times n}, d \in \mathbb{R}^m$. I find the ...