Not sure if this will ring a bell. There are many problems similar to the assignment problem nested in my objective function. These problems are formulated as linear programming problems. And the solutions are the indices of certain elements in a matrix, which make the objective function non-differentiable.
A smooth and differentiable relaxation of the assignment problem is to solve an entropically regularize optimal-transport problem.
Edit: chapter 4 in the book below is perhaps a better reference for this
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Hi Fredrik, thank you so much! Let me take a look. (I guess this may improve the speed of solving my linear programming problem. But since I need the matrix index as an intermediate output in my objective function, this may not solve the issue.)
Hi @stevengj, could you suggest the best 2-3 derivative free algorithms from NLopt.jl according to your tests?
Thank you!
And whether they are available for JuMP as well 
Any up-to-date source would be welcomed.
Hi bboptimize now provdes initial guess https://github.com/robertfeldt/BlackBoxOptim.jl which is great