VLSI CAD Flow: Logic Synthesis, Placement and Routing 6.375 ...

Quadratic Optimization Problem
E
D
( ρ , ρ
)
' '
v u
F
A
B
C
A
( l
)
M ⎡M
ρ
⎢
= ⎢*
ρ'⎢0
⎢
M ⎣M
Linearly constrained quadratic programming problem
min{
Φ(
x)
x∈R
m
s.t.
=
x
T
C
x
+ d
( l ) x u(
l
A =
ρ ) ( uρ
, v
)
T
x }
A
B
M
*
0
M
C
M
*
0
M
D
M
0
*
M
E
M
0
*
M
F
M
0
*
M
G
M ⎤
⎥
L⎥
L⎥
⎥
M ⎦
Accounts for fixed modules
Wire-length for movable modules
Center-of-gravity constraints
Problem is computationally tractable, and well behaved
Commercial solvers available: mostek