# Questions tagged [totally-unimodular]

The tag has no usage guidance.

5 questions
Filter by
Sorted by
Tagged with
1 vote
96 views

### 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 ...
240 views

### 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 ...
187 views

### Assignment problem with mutually exclusive constraints has an integral polyhedron?

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