Digital Signal Processing Reference
In-Depth Information
Optimizationwith equality and
inequality constraints
22.1 Introduction
If we have an objective function to be optimized under an equality constraint,
we use the Lagrange multiplier method and set up a Lagrangian which is then
differentiated and set to zero to obtain a set of necessary conditions for an
extremum. If there are inequality constraints as well, then a further modification
is necessary. The resulting necessary conditions for optimality are called the
Karush-Kuhn-Tucker (KKT) conditions. Essentially we add another term to
the Lagrangian involving what is called a
KKT multiplier
. We explain the idea
briefly here. There are several references dedicated to a detailed discussion of
this topic; for example, see Luenberger [1969], Chong and
Zak [2001], Boyd and
Vandenberghe [2004], or Antoniou and Lu [2007].
22.2 Setting up the problem
The optimization problem to be addressed here is as follows:
f
(
x
) =
f
(
x
0
,x
1
,...,x
N−
1
)
,
minimize
(22
.
1)
subject to
M
equality constraints,
h
(
x
)=
0
,
(22
.
2)
730
Search WWH ::
Custom Search