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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?

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    $\begingroup$ No for BARON .. $\endgroup$
    – Mark L. Stone
    Oct 28 '20 at 18:56
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    $\begingroup$ Hello Alberto. Why do you have an exponential number of constraints? Would be nice if you give some words about the original problem behind the model you described. Just to understand if another formulation can be of interest. And also because we would like to benchmark LocalSolver on this interesting, challenging problem. $\endgroup$
    – LocalSolver
    Oct 30 '20 at 20:53
  • $\begingroup$ @LocalSolver a typical example would be subtour elimination constraints in a routing problem. Alternative formulations (such as MTZ) have notoriously poor continuous relaxations. $\endgroup$
    – Alberto Santini
    Oct 30 '20 at 21:16
  • $\begingroup$ Sorry to be so curious, but what is the definition of the y variables in the model? $\endgroup$
    – LocalSolver
    Oct 31 '20 at 8:49

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