It seems like when the KKT conditions were first developed, these were very useful for determining whether the solution to a optimization problem was optimal or not.
However, it seems like nowadays, we hear about the KKT Conditions less - for instance, when reading about all the cool things that Deep Neural Networks are doing (e.g. AlphaGO, Protein Folding, Self Driving Cars) , the KKT Conditions never seem to be mentioned that much.
I was wondering if someone could comment on the following:
With the advent of approximate optimization methods such as Gradient Descent that seem to work quite well for non-convex and high dimensional problems - do the KKT Conditions have as much importance in Optimization now as they did when they were first developed?