I am solving a non-linear mixed-integer programme with BARON. The objective function looks like $\big( \sum_i x_i \big) \cdot \big(\prod_i e^{-y_i}\big)$ (binary $x$ and real-valued $y$) and it has some quadratic constraints.
My problem is that I have an exponential number of linear constraints. I would like to add them in a way analogous to the Lazy Constraint callbacks of CPLEX and Gurobi. Does Baron support anything like this? Are there other solvers which allow lazy constraints and also have out-of-the-box support for weird non-linearities such as the above ones?