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Mathematical Description of LP

A linear programming (LP) problem has 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 variables and constraints, then the formal statement of the problem solved by PROC INTPOINT is

where

• is the variable objective function coefficient vector
• is the variable value vector
• is the constraint coefficient matrix for the variables, where is the coefficient of variable in the th constraint
• is the side constraint right-hand-side vector
• is the variable lower bound vector
• is the variable upper bound vector