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4 votes
1 answer
866 views

When is a triangular matrix totally unimodular?

I have a {0,1}, invertible, triangular matrix, that I would like to show is totally unimodular. Are there any known results on the total unimodularity of classes of triangular matrices?
0 votes
0 answers
108 views

Solutions to matrix equations in the non-negative integers

For an integer matrix $S$, and an integer vector $y$, I'm looking for solutions to $xS = y$ where the entries in $x$ are in the non-negative integers. I've been doing this with Sage's mixed integer ...
0 votes
0 answers
369 views

Finding a point in the relative interior of the convex hull of a set of integer-valued vectors

Let $X \subset \mathbb{Z}^n$ be the set of integer-valued vectors satisfying a system of linear constraints. We can suppose that $X$ is the set of integral points in a given polyhydral set $Y \subset \...
2 votes
0 answers
80 views

Making a polyhedron integral by selecting value for a specific co-ordinate of constraint vector

I am currently trying to solve a binary integer programming(maximization) problem, where the first row of the constraint matrix corresponds to the constraints on the total number of 1's in the vector ...
0 votes
0 answers
68 views

A seemingly easy integer programming question

Let $k, m \in \mathbb{Z}_{ > 1}$. Let $a \in \mathbb{Z}_{> 0}^m$ and $t \in \mathbb{Z}^k$. Let $\varepsilon = (\varepsilon_{i,j})_{1 \leq i \leq m \\1 \leq j \leq k}$ be a matrix with entries in ...
6 votes
1 answer
1k views

Speed up Linear programming

I have a linear programming problem like this: minimize $c^t X$ under the constraint that $AX \ge b$. I will need to solve this linear programming problem online many times. I need it to be as fast ...
2 votes
1 answer
143 views

Find base of kernel with as many 0 as possible

I have a 400x132 rectangular matrix with only 0 and 1. I am looking for the linear combinations of the columns of the matrix that sum to 0. For example C1 + C2 - C3 = 0. I want to find the linear ...