How to express AND OR NOT in constraints?

like this ‘U(4,i) == 0 | U(4,i) == exp(-X_0(7,i)) * (1 - (X(7,i) - X_0(7,i)))’.

Just expressing boolean operations can be done with mixed-integer programming like shown here

However whether you will be able to fit your problem in this framework depends on which of X, X_0 are variables and which are constants. You need to keep it linear.