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.

this package contains the documentation for the lp_solve program and the library.

homepage http://www.geocities.com/lpsolve/