Guaranteed Constrained and Unconstrained Global Optimisation in Julia | D.P. Sanders | JuliaCon 2019

Speaker: David P. Sanders

Set computations with interval arithmetic allow us to write surprisingly efficient software for guaranteed unconstrained and constrained global optimisation in pure Julia.

[haoli]

This is a very clever idea I think. Works in a similar way like Implicit plot.

[sammathew]

I don't understand why the Ipopt result is infeasible, since x1 is lower bounded on 2.
For minimizing the objective: x1^2 + x2^2 + x3^4 - x4^7 -200x5 - x6^5 - x7^9 + x8^5 - 8x9^3,
given that all variables are greater than 1, in order to minimize, all variables who have a positive coefficient will be pinned to their lower bound, while all those that are negative, will be fixed on their upper bound.
I understand though that the objective contains some numerical errors, if we simply plug the the optimum values of the variables into the objective function. But I'm not sure to call it infeasible solution!