What is the proper way of studying chess?

What I do is either choose a position from Grandmaster Prep:Calculation and try and solve it or go through games of some tactical and positional players like Aronian, Caruana, Ivanchuk, Kramnik and then try and figure out why they made some moves.

However, my question is what is the optimal way of studying chess which guarantees the most improvement in the shortest period of time?

That's easy.  Step one is to become fabulously wealthy.  Now hire a chess coaching staff and study and play chess all day long.  My point though is that someone has to point out what your individual weaknesses are so my vote is to hire a coach.  Long term it sounds like you have a great way to study but "most improvement in the shortest period" probably requires more focus.  Of course if you have the time to study all the videos and chess mentor lessons that are available to a diamond member, it's kind of like being rich and having a live in chess staff.  

Below about 1800 (OTB), the quickest way to improve is lots and lots of tactics puzzles. And play lots of slow games, focusing on your thought process. Of course, then you'll reach 1800 and realize that there's more to chess than just tactics, so you'll have to study other areas of the game to improve any further.

Regular use of a sacrificial altar surrounded by concentric circles and elaborate geometric designs.

"... This book is the first volume in a series of manuals designed for players who are building the foundations of their chess knowledge. The reader will receive the necessary basic knowledge in six areas of the game - tactcs, positional play, strategy, the calculation of variations, the opening and the endgame. ... To make the book entertaining and varied, I have mixed up these different areas, ..." - GM Artur Yusupov

Yes I hvae five of Yusupov's books and I must say they are really good.