Trying to solve an MINLP optimization problem which needs defining two disjunctive, semi continuous, and unrestricted in sign variables.

As far as I know I have to be able to use binary variables (refer to programming books by Eiselt), and I've seen people suggesting that it can be done in IBM ILOG CPLEX or GAMS, but can I do such thing in MATLAB?

Thanks in advance

P.S. I haven't tried GAMS and CPLEX and I'm not sure if that's possible or not

EDIT: I tried BARON and DICOPT solvers in GAMS but they couldn't handle the nonlinear constraint, and they even suggested using binary variables, so I'm restricted to binary variables and there's no more non-linearity .