Optimization

93

4

Linear Programming

4.1 Introduction

Linear programming refers to an optimization problem that has the objec-

tive and the constraints as a linear function of the design variables. The con-

straints could be of an equality or inequality type or both. Mathematically, a

linear function satises the following properties:

f(x + y) = f(x) + f(y) (4.1)

f(kx) = kf(x) (4.2)

where x and y are the variables and k is a scalar. A practical linear program-

ming problem (LPP) might contain hundreds of design variables and con-

straints and thus require special solution techniques that are different from

the methods that were described in the previous ...