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In robust optimization, the true return is not known, we just have a prior $\alpha$ and you have to take into account a possible misestimate which can lower the true return. This is done under the assumption that the posterior return will be within the prior return $\alpha$ plus minus the error being in some $\sigma$-interval. Now a try for a more formal ...

From a general point of view and to answer directly to your originial question, you should only have to modify the inputs to the MATLAB function you refer to. As a matter of fact, fmincon is an optimizer looking to process a broad variety of problems as explained in the documentation: fmincon attempts to find a constrained minimum of a scalar function of ...