I am using FindMinimum to get a local minimum to a non-liner function of 50 variables on [0,1]^50 with some additional constraints. I provide FindMinumum with a feasible point which reaches a function value of 0.74 and surprisingly FindMinimum get me as answer another feasible but with a worse value of 0.81 (after 500 iterations with the message: FindMinimum::cvmit: Failed to converge to the requested accuracy or precision within 500 iterations.
I do not understand why the algorithm is providing a worse answer than the one provided by the initial point. I have tried different choices for the Method but with similar behavior, so:
Can someone provide an explanation or suggest how to proceed?
Many thanks in advance.