I think you want to use a global nonlinear optimizer. For instance, BMIBNB under YALMIP (which in turn needs a local nonlinear solver, such as FMINCON, to call) or BARON. Perhaps COUENNE or SCIP global solver would work as well. Depending on the values of alpha and beta, there may be many global optima. This is actually quite an easy problem, especially in 2 dimensions.
If you use a local nonlinear solver, you may find a local optimum which is not globally optimal. That might not meet your needs. You are especially likely to be led astray if you use a starting value for x of zeros(n,1), which might get stuck at that point, which is actually the global minimum, not even a local maximum, and might get erroneously reported as being a local optimum based on looking only at first order optimality conditions.