mixed-integer nonlinear optimization of objective function with undefined coefficients

Hi everyone,

Consider i have an [objective function = A(X1)+B(X2)+C(X3)+.... ] where X1,X2,X3,... are the inputs,

where A,B,C,.. are not constants and non-linear but their values changes according the X1,X2,X3,... values,

X1,X2,X3,... are binary values either 1 or 0,

Also one of the constraints is the determinant value of a matrix that include the inputs X1,X2,X3,..

So can i still use any of mathematical optimization methods in optimization tool box to solve this kind of problem ? considering it should be a mathematical method and not heuristic such GA,

and what is the best method to solve this kind of problem ?

N.B: am not very expert at using matlab

Thanks.