I use
NMinimize[someFunction, Method -> {"RandomSearch", Method ->{"InteriorPoint"},"SearchPoints" -> 2n, "RandomSeed" -> RandomInteger[{0, 100}], "PostProcess" -> {FindMinimum, Method -> "QuasiNewton"}}, MaxIterations -> 1000 n, PrecisionGoal -> 10, AccuracyGoal -> 10]`
where someFunction is a function of n variables.
How could I measure the time complexity of this method?
Answer
There is a nice function BenchmarkPlot

The usage is something like this
Needs["GeneralUtilities`"]
BenchmarkPlot[{f1,f2}, # &, PowerRange[1, 1000], "IncludeFits" -> True]
Typical output:

There are already many examples on MMA.SE.
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