The uniqueness of a solution depends on the function being optimized, not the particular choice of an optimization routine. In general, if you start near a local optimum, you will converge to that optimum (but the beautiful fractals for Newton's iteration show that this is not always the case!) If your function has several local maxima and you want to find the one that is the global maximum, you can try using initial conditions on a uniform grid in parameter space, as detailed in this article: How to find an initial guess for an optimization - The DO Loop
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