# Questions tagged [totally-unimodular]

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### Total Unimodularity of constraint matrix

Given a directed graph $G=(V,E)$, I have the following integer program- \begin{align} \max & \sum_{(u,v) \in E} \sum_{s \in S} w_{uv} z_{uv,s} + \sum_{v \in V} \sum_{s \in S} b_{v,s} x_{v,s} \\ \...
• 223
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### Why do I get a binary solution even when I solve an LP problem with continuous variables?

I have a MILP in the following form maximize $${\bf c}^T{\bf x}$$ subject to $${\bf Ax}\le {\bf b}$$ Matrix ${\bf A}$ is a binary matrix, and very sparse. It is a larger matrix with 300 rows and 1000 ...
• 2,377
1 vote
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### Converting a Linear Program with TU Constraint Matrix to a Nonlinear Convex Model: Solver Performance?

I'm currently working on a large Mixed Integer Program (MIP) where the constraint matrix is Totally Unimodular (TU), allowing me to model it as a Linear Program (LP) for efficiency, as total ...
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### Can we add a certain binary row to a matrix which preserves total unimodularity?

Suppose I have a matrix $A\in \{-1, 0, 1\}^{m\times n}$ which is Totally Unimodular (TU), and a vector $b^T \in \{-1, 0, 1\}^{1\times n}$ which has exactly one entry which is $1$ and exactly one entry ...
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### Assignment problem with mutually exclusive constraints has an integral polyhedron?

I have the following problem $\min \sum_{i\in I} \sum_{j \in J} c_{ij} x_{ij}$ $s.t. \sum_{j \in J} x_{ij} \leq b_i, \forall i \in I$ $\sum_{j \in S_l} x_{ij} \leq 1, \forall l \in L, i \in I$ \$\...
• 33