## Version 1.2.0

• Single
• Double

### LA04 Sparse linear programming: steepest-edge simplex method

This package uses the simplex method to solve the linear programming problem

subject to the constraints

 ${l}_{j}\le {x}_{j}\le {u}_{j},1\le j\le k,$ (1)

${x}_{j}\ge 0,l\le j\le n.$

The variables ${x}_{j}$, $k+1\le j\le l-1$, if any, are free (have no bounds). Full advantage is taken of any zero coeﬃcients ${a}_{ij}$. The inequalities $0\le k must hold. Special values ${l}_{i}=-\sigma$ and ${u}_{i}=\sigma$ may be used in (1) to remove one or both bounds.

To accommodate roundoﬀ, all variables are permitted to lie slightly outside their bounds.

Precision: At least 8-byte arithmetic is recommended.