Iterations and Function Counts - MATLAB & Simulink (original) (raw)
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In general, Optimization Toolbox™ solvers iterate to find an optimum. A solver begins at an initial value_x_0, performs some intermediate calculations that eventually lead to a new point_x_1, and then repeats the process to find successive approximations _x_2,_x_3, ... of the local minimum. Processing stops after some number of iterations k.
You can limit the number of iterations or function counts by setting theMaxIterations or MaxFunctionEvaluations 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. SeeSet 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, e_i_ represents the unit vector in the_i_th 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, theF-countcan be significantly less than the total number of function evaluations.
Sometimes a solver attempts a step and rejects the attempt. Thetrust-region, trust-region-reflective, andtrust-region-dogleg algorithms count these failed attempts as iterations, and report the (unchanged) result in the iterative display. Theinterior-point, active-set, andlevenberg-marquardt algorithms do not count failed attempts as iterations, and do not report the attempts in the iterative display. All attempted steps increase the F-count, regardless of the algorithm.
F-count is a header in the iterative display for many solvers. For an example, see Interpret Result.
The F-count appears in the output structure asoutput.funcCount, enabling you to access the evaluation count programmatically. For more information, see Output Structures.