Wireless Sensor and Actuator Networks for Lighting Energy ...

The optimization problem in (3.16) is called a linear programming problem if
the objective function and the constraint functions are linear, i.e.
f i
(x + y) = f i
(x) + f i
(y), i = 0,…,m. (3.18)
The standard form of a linear programming problem is formulated as (3.19):
minimize
subject to
c 1
x 1
+ c 2
x 2
++ c n
x n
a 11
x 1
+ a 12
x 2
++ a 1n
x n
b 1
a 21
x 1
+ a 22
x 2
++ a 2n
x n
b 2
(3.19)
a m1
x 1
+ a m2
x 2
++ a mn
x n
b m
x 1
, x 2
, x n
0,
or in matrix representation:
minimize
subject to
c T x
Ax b
x 0,
(3.20)
where
c = [ c 1
c 2
c n ] T
x = [ x 1
x 2
x n ] T
a 11
a 12
a 1n
a 21
a 22
a
2n
A =
a m1
a m2
a mn
b = [ b 1
b 2
b n ] T .
Linear programming problems have been well-studied, and various algorithms
have been proposed with different levels of efficiency and complexity. The earliest and
yet still most popular solver for linear programming problems is the simplex algorithm
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