Linear Programming and Extensions
One of the areas of mathematics which has extensive use in combinatorial optimization is called linear programming (LP). It derives its name from the fact that the LP problem is an optimization problem in which the objective function and all the constraints are linear. Many real-world problems can be formulated in this way. Even more problems can be effectively approximated by an LP model. Also an LP solution method can be used as a subroutine in solving integer-programming problems (as indicated in Section 2.1) and certain nonlinear optimization problems.
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