How to address Non Convex optimization in deep learning?

Question

I am working on a non-convex optimization these days and the question comes to my mind about the application of non-convex optimization in deep learning. How can be sure that our objective function is convex? Thanks

Answer 1

The standard definition is if f(θx + (1 − θ)y) ≤ θf(x) + (1 − θ)f(y) for 0≤θ≤1 and the domain of x,y is also convex.

So if you could prove that for your function, you would know it's convex.

In deep learning its very difficult to be sure that your objective function is Non Convex thats why initialization and hyperparameter tuning becomes very important