[1] https://papers.nips.cc/paper/4443-algorithms-for-hyper-param...
Not only that it can be done, but it works even by random trial. Sophisticated optimization techniques work out just 2x faster, so if you have cheap GPU, you can run 2x more trials and get your hyperparameters fine tuned.
If you want to apply optimization, you can use one of the popular libraries like hyperopt and MOE.
ok, well, imagine (for simplicity) that you are standing on a 3d-surface with mountains and valleys and such. you can only see so far. you need to walk/run etc. to get to a pot of gold which is there at the global minima of this landscape.
what do you do ? one option is choose gradient descent :) start walking somewhere, and see if the your height, from your previous position, is decreasing. if it is, then maybe you are on the right track...