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# Questions tagged [integer-programming]

Questions on optimization constrained to integer variables.

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### Characterizing the Result of Lift and Project Method for Integer Programming

I have the following integer linear programming problem: Let $P=\{x\in \mathbb{R}^n\colon Ax\geq b\}\subseteq [0,1]^n$ be a polytope. For a fixed index $j\in [n]$, consider the polyhedron $P^j$ ...
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### Chvatal-Gomory integer rounding method to find facets of $\operatorname{conv}(S)$

The question: "given a set $S = \{x \in \mathbb{Z}^2 : 4x_1 + x_2 ≤ 28, x_1 + 4x_2 ≤ 27, x_1 − x_2 ≤ 1, x ≥ 0 \}$. we are tasked with deriving each facet of $\operatorname{conv}(S)$ as a Chvatal-...
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### Will Branch and Bound always terminate after finite iterations?

I learnt this algorithm by a simple example illustrating the essential ideas of it without analyzing in details. So my questions are Will BB always end after finite iterations? (Both for binary cases ...
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### Reference Request: Vertex Enumeration Algorithms That Finds All Integer Points in a Polytope

For fun, I explored vertex enumeration algorithms for linear programs to find all feasible extreme points in a polytope. Naturally, I asked, "Do there exist algorithms that solve for all integer ...
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