In general, Optimization Toolbox™ solvers iterate to find an optimum. This means 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.
At any step, intermediate calculations may involve evaluating
the objective function and constraints, if any, at points near the
current iterate xi. For
example, the solver may estimate a gradient by finite differences.
At each of these nearby points, the function count (F-count) is increased by one.
If there are no constraints, the F-count reports
the total number of objective function evaluations.
If there are constraints, the F-count reports
only the number of points where function evaluations took place, not
the total number of evaluations of constraint functions.
If there are many constraints, the F-count can
be significantly less than the total number of function evaluations.
F-count is a header in the iterative display
for many solvers. For an example, see Interpreting the Result.
The F-count appears in the output structure
as output.funcCount. This enables you to access
the evaluation count programmatically. For more information on output
structures, see Output Structures.
Sometimes a solver attempts a step, and rejects the attempt.
The trust-region, trust-region-reflective,
and trust-region-dogleg algorithms count these
failed attempts as iterations, and report the (unchanged) result in
the iterative display. The interior-point, active-set,
and levenberg-marquardt algorithms do not count
such an attempt as an iteration, and do not report the attempt in
the iterative display. All attempted steps increase the F-count,
regardless of the algorithm.