
Interior Point Methods 227
That is, y is the average value of the terms x
i
z
i
. A smaller average indicates
more proximity to optimality. Then
µ = τy,
and thus (6.12) becomes
0 A
T
I
A 0 0
Z 0 X
d
x
d
π
d
z
=
0
0
−XZe + τye
. (6.13)
The centering parameter τ can be selected to be less than or equal to
1 (but greater than or equal to 0) to allow a tradeoff between moving toward
the central path and reducing y.
6.3.2 General Primal-Dual Interior Point Method
We now present the general primal-dual interior point framework. The general
iterative strategy is a follows.
Step 0: Obtain an initial interior primal-dual solution (x
(0)
, π
(0)
, z
(0)
) such
that x
(0)
> 0, z