Solving Large-scale MINLP problem

[Tooran BM]

Hi Johan

I am solving a large-scale non-linear problem. Among the variables, there are two variables x and y that cannot be non-zero at the same time. So, I introduced a binary variable d and the following constraints:

0 <= x <= x_max*d

0 <= y <= y_max*(1-d)

However, this will result in a MINLP that is not supported by many solvers. I am using Gurobi and it takes a long time to return a solution or reach the stopping criteria with a large gap and thereby no good solution. May I have your help with the two following points:

1. Could you please introduce some local solvers that can solve MINLP? As global optimality is not the main problem now.

2. What if I remove the binary variable and add a constraint like x*y==0 and use other solvers like ipopt. 

Thank you

  

[Johan Löfberg]

If you don't want  globally certified solution, use a global solver but set termination criteria extremely weak so that it terminates immediately when it has found a solution

...or just try with a nonlinear solver and the nonconvex x*y==0 

i.e. you basically answered your own question already