For "on-line" work:
- your minimizer must find a solution within bounded time, or else you must be willing to accept the best solution it found within the bounded time.
- your minimizer must never crash, or else your computing infrastructure must catch and gracefully handle every such crash
- as there is a possibility that every invocation of the minimizer might crash or time out, there must be a "safe" value you can use or safe action you can take if it crashes or times out over the entire period
- your function must have a single minima within the solution bounds, or if it has multiple identical minima within the solution bounds, then any of them must be acceptable; OR, if your function may have multiple different minima within the solution bounds, then it must be acceptable that you do not find the global minima within the allotted time.
fmincon is not suitable for cases in which you have multiple minima and you need to find the global minima -- fmincon cannot even try to handle that: fmincon finds a single minima and returns it no matter how bad it is.
GA at least tries to find global minima (but it cannot promise to succeed.) GA usually needs considerably more function iterations (so more time.)
MATLAB is not able to promise that either fmincon or GA will finish even a single iteration within any fixed period of time, and it takes fancy (and not completely reliable) mechanisms in order for MATLAB to interrupt an iteration and force it to terminate. Those termination mechanisms are not supported in MATLAB: you would have to do some work at the C level to kick the appropriate operating system facilities. Not, in other words, suitable for most "on-line"work.
MATLAB is also not able to gracefully handle crashes involving memory corruption or running out of memory. Again this makes it risky to use for "on-line" work.
There is no known minimizer in any computer language that is reliably able to find global minima of general functions. My memory tells me that there is a strong computing theory that says that a generalized global minima finder is impossible.
If one knows the form of the equations ahead of time, and knows what the varying parameters are, then it might be possible to construct a global minimizer for that restricted set of problems.
