It is hard to know in advance which algorithm will be faster. Generally, the more information you can give to an algorithm (explicit gradient, Hessian sparsity, etc.), the faster the computation, but there are counterexamples. The fmincon trust-region-reflective algorithm is essentially the same as the fminunc trust-region algorithm, so there is no point trying both. But the fmincon sqp and interior-point algorithms are different, though sqp is not large-scale.
One of the most important things is to give a good initial guess, and that is often very difficult to obtain.
If the problem has no constraints, but you can prove that the solution lies in a bounded region, then it is almost certainly better to give the bounds explicitly and to use fmincon.
Good luck,
Alan Weiss
MATLAB mathematical toolbox documentation
