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# Package: lp-solve (5.5.0.15-4 and others)

## Solve (mixed integer) linear programming problems

The linear programming (LP) problem can be formulated as: Solve A.x >= V1, with V2.x maximal. A is a matrix, x is a vector of (nonnegative) variables, V1 is a vector called the right hand side, and V2 is a vector specifying the objective function.

An integer linear programming (ILP) problem is an LP with the constraint that all the variables are integers. In a mixed integer linear programming (MILP) problem, some of the variables are integer and others are real.

The program lp_solve solves LP, ILP, and MILP problems. It is slightly more general than suggested above, in that every row of A (specifying one constraint) can have its own (in)equality, <=, >= or =. The result specifies values for all variables.

lp_solve uses the 'Simplex' algorithm and sparse matrix methods for pure LP problems. If one or more of the variables is declared integer, the Simplex algorithm is iterated with a branch and bound algorithm, until the desired optimal solution is found. lp_solve can read MPS format input files.

Tags: Field: Mathematics, Role: Program, Scope: Application

## Other Packages Related to lp-solve

 depends recommends suggests enhances
• dep: libc6 (>= 2.14) [amd64]
GNU C Library: Shared libraries
also a virtual package provided by libc6-udeb
dep: libc6 (>= 2.17) [arm64, ppc64el]
dep: libc6 (>= 2.7) [not amd64, arm64, ppc64el]
• dep: libcolamd2 (>= 4.5.2)
column approximate minimum degree ordering library for sparse matrices