diff --git a/content/numerical/IntegerLinearProgramming.h b/content/numerical/IntegerLinearProgramming.h new file mode 100644 index 000000000..7317a482b --- /dev/null +++ b/content/numerical/IntegerLinearProgramming.h @@ -0,0 +1,9 @@ +/** + * Author: Iván Renison + * Date: 2024-12-08 + * Source: Wikipedia + * Description: When $A$ and $b$ have all integer entries and $A$ is totally unimodular then + * every basic feasible solution is integral so the simplex algorithm can be used to solve ILP. + * A matrix $A$ is totally unimodular if every square submatrix of $A$ has determinant $0$, $1$ or $-1$. + * Status: untested + */ diff --git a/content/numerical/chapter.tex b/content/numerical/chapter.tex index 04c91fff6..63e922d20 100644 --- a/content/numerical/chapter.tex +++ b/content/numerical/chapter.tex @@ -14,6 +14,7 @@ \section{Optimization} \kactlimport{Integrate.h} \kactlimport{IntegrateAdaptive.h} \kactlimport{Simplex.h} + \kactlimport{IntegerLinearProgramming.h} \section{Matrices} \kactlimport{Determinant.h}