eldo_user

Optimization
Eldo Optimizer/Search Algorithm
The algorithm FIND_ZERO aims to find a solution to:
Find x such that F(x) = 0, where a ≤ x ≤ b.
Using a SPICE formulation:
.OPTIMIZE METHOD=SEARCH
* Design variable specification
.PARAMOPT X=(X0, A, B)
* Goal value
.OBJECTIVE LABEL=F_R GOAL=R
Note
Specifying a weight number with WEIGHT=μ r is allowed, however, it is not considered. A
warning message is generated.
F(x) = f r (x) − r defines the difference between the actual measure f r and the goal value r.
The search method enables you to specify an initial guess point to locate an interval for a
solution if one has not been specified:
• When the interval [a, b] is not known, a guess point x0 must be specified with the
.PARAMOPT command: .PARAMOPT x=(x0,*,*). The method initially invokes a
search phase to find an interval for locating a solution.
• When the interval [a, b] is specified, the guess point is not used and the method directly
starts the search for a solution.
The FIND_ZERO algorithm uses a combination of dichotomy, secant, and inverse quadratic
interpolation methods. It defines a zero as a point where the function crosses the x-axis. Points
where the function touches but does not cross (see Figure 13-5) the x-axis are not valid zeros.
For example, F(x) = x 2 is a parabola that touches the x-axis at (0, 0). Since the function never
crosses the x-axis, no zero is found. For functions with no valid zeros, FIND_ZERO executes
until an undefined value is detected.
Figure 13-5. Non-Valid and Valid Zeros
Eldo® User's Manual, 15.3 627