The number of iterations in an optimization depends on a solver's stopping criteria. These criteria include several tolerances you can set. Generally, a tolerance is a threshold which, if crossed, stops the iterations of a solver.
Set tolerances and other criteria using optimoptions
as
explained in Set and Change Options.
Tip
Generally set tolerances such as 
You can find the default tolerances in the Optimization App. Some default tolerances differ for different algorithms, so set both the solver and the algorithm.
optimoptions
displays tolerances.
For example,
options = optimoptions('fmincon');
[options.OptimalityTolerance,options.FunctionTolerance,options.StepTolerance]
ans = 1.0e06 * 1.0000 1.0000 0.0001
You can also find the default tolerances in the options section of the solver function reference page.
StepTolerance
is a lower bound
on the size of a step, meaning the norm of (x_{i} – x_{i+1}).
If the solver attempts to take a step that is smaller than StepTolerance
,
the iterations end. StepTolerance
is sometimes
used as a relative bound, meaning iterations
end when (x_{i} – x_{i+1}) < StepTolerance
*(1
+ x_{i}),
or a similar relative measure.
For some algorithms, FunctionTolerance
is
a lower bound on the change in the value of the objective function
during a step. For those algorithms, if f(x_{i}) – f(x_{i+1}) < FunctionTolerance
,
the iterations end. FunctionTolerance
is sometimes
used as a relative bound, meaning iterations
end when f(x_{i}) – f(x_{i+1}) < FunctionTolerance
*(1
+ f(x_{i})),
or a similar relative measure.
Note:
Unlike other solvers, 
OptimalityTolerance
is a tolerance
for the firstorder optimality measure. If the optimality measure
is less than OptimalityTolerance
, the iterations
end. OptimalityTolerance
can also be a relative
bound on the firstorder optimality measure. Firstorder optimality
measure is defined in FirstOrder Optimality Measure.
ConstraintTolerance
is an upper
bound on the magnitude of any constraint functions. If a solver returns
a point x with c(x) > ConstraintTolerance
or ceq(x) > ConstraintTolerance
,
the solver reports that the constraints are violated at x. ConstraintTolerance
can
also be a relative bound.
Note:

MaxIterations
is a bound on the
number of solver iterations. MaxFunctionEvaluations
is
a bound on the number of function evaluations. Iterations and function
evaluations are discussed in Iterations and Function Counts.
There are two other tolerances that apply to particular solvers: TolPCG
and MaxPCGIter
.
These relate to preconditioned conjugate gradient steps. For more
information, see Preconditioned Conjugate Gradient Method.
There are several tolerances that apply only to the fmincon
interiorpoint
algorithm. For more information, see InteriorPoint
Algorithm in fmincon
options
.
There are several tolerances that apply only to intlinprog
.
See Some "Integer" Solutions Are Not Integers and Branch and Bound.