Mathematical Description of LP

The INTPOINT Procedure

Mathematical Description of LP

PROC INTPOINT solves LP problems. These have a linear objective function and a collection of linear constraints. PROC INTPOINT finds the values of variables that minimize the total cost of the solution. The value of each variable is on or between the variable's lower and upper bounds, and the constraints are satisfied.

If an LP has g variables and k constraints, then the formal statement of the problem solved by PROC INTPOINT is

: min {d^T z}
subject to: $Q z \geq,=, \leq r$
: $m \leq z \leq v$

where

: d is the g x 1 objective function coefficient of the variables vector
: z is the g x 1 variable value vector
: Q is the k x g constraint coefficient matrix for the variables, where Q_i,j is the coefficient of variable j in the ith constraint
: r is the k x 1 side constraint right-hand-side vector
: m is the g x 1 variable value lower bound vector
: v is the g x 1 variable value upper bound vector

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