User Guide

4
-
6 Understandin
g
Optimization Principles and Options
Active and Inactive Constraints
An active constraint is one which affects the solution of the
optimization problem—that is, the solution would probably be
different if the constraint were removed. Equality constraints are
always active (e.g., a constraint of the form V
out
= 3.75 V is
always active). Inequality constraints are considered active if
the solution violates the constraint or if it is equal to the
constraint (e.g., a constraint of the form R
eq
>= 100 is active if
R
eq
is less than or equal to 100 at the solution).
La
g
ran
g
e Multipliers
The result of a constrained optimization is typically a
compromise between further reduction of the goals and
violation of one or more constraints. A set of numbers—the
Lagrange multipliers—provide valuable information about the
tradeoffs between the goals and the constraints.
The PSpice Optimizer calculates Lagrange multipliers only for
those constraints which are active at the solution. A constraint
which is inactive can be removed from the problem without
affecting the solution, which means there is no tradeoff between
the goals and the constraint.
Think of Lagrange multipliers as the incremental cost of each
active constraint on the solution.
Example: Consider optimizing propagation delay through a gate
subject to a constraint on gate width and a constraint on bias
current. Suppose that at the optimum, both constraints are
active. There are two Lagrange multipliers for this problem:
• Incremental cost of propagation delay versus gate width.
• Incremental cost of propagation delay versus bias current.
For this problem, the units of the Lagrange multipliers are
seconds/meter and seconds/ampere, respectively.
In a problem with several goals which have been combined as a
sum-of-squares, the target value is dimensionless. In this case,
To view La
g
ran
g
e multipliers for
your desi
g
n,
g
enerate a report by
selectin
g
Reports from the File
menu and browse the
desi
g
n_name .oot report file.
See
Producing Optimization
Reports on page 3-26 for
instructions.