Iterations and Function Counts
In general, Optimization Toolbox™ solvers iterate to find an optimum. A solver begins at an initial value x0, performs some intermediate calculations that eventually lead to a new point x1, and then repeats the process to find successive approximations x2, x3, ... of the local minimum. Processing stops after some number of iterations k.
You can limit the number of iterations or function counts by setting the
options for a solver using
optimoptions. Or, if you want a solver to
continue after reaching one of these limits, raise the values of these options. See
Set and Change Optimization Options.
At any step, intermediate calculations can involve evaluating the objective function
and any constraints at points near the current iterate
xi. For example, the solver might
estimate a gradient by finite differences. At each nearby point, the function count
F-count) increases by one. The figure Typical Iteration in 3-D Space shows that, in 3-D
space with forward finite differences of size delta, one iteration typically corresponds
to an increase in function count of four. In the figure,
ei represents the unit vector in the
ith coordinate direction.
Typical Iteration in 3-D Space
If the problem has no constraints, the
F-countreports the total number of objective function evaluations.
If the problem has constraints, the
F-countreports only the number of points where function evaluations took place, not the total number of evaluations of constraint functions. So, if the problem has many constraints, the
F-countcan be significantly less than the total number of function evaluations.
Sometimes a solver attempts a step and rejects the attempt. The
trust-region-dogleg algorithms count these failed attempts as
iterations, and report the (unchanged) result in the iterative display. The
levenberg-marquardt algorithms do not count failed attempts as
iterations, and do not report the attempts in the iterative display. All attempted steps
F-count, regardless of the algorithm.
F-count is a header in the iterative display
for many solvers. For an example, see Interpret Result.
F-count appears in the output structure as
output.funcCount, enabling you to access the evaluation count
programmatically. For more information, see Output Structures.