What is a strategy to do theoretical research?

In mathematics, a paper with 20 pages of proofs does not have twenty pages of original ideas. It might have a page worth, maybe. The rest are combinations of 2-6 previously known ideas, often with little or no acknowledgements of their first appearance [footnote 1].

To beginning graduate students, I strongly suggest to read much older papers. They are usually much shorter, much simpler, and actually allow to learn ideas in their simplest. In my branch of mathematics, that means papers that are at least 30 years old. General useful mathematical background papers go at least 60-100 years.

A good way of doing research is just to be curious --- after all this is what got you into the position you are now, right? Whenever you are curious about something, try figuring it out, look for some way of doing it, search references, read whatever looks interesting, swear at whatever does not. Keep journal with your questions, observations, dead-ends, ideas and swearing. Occasionally, when there is something particularly nice, add those 5, 10 or 15 pages of formal expository and technical scaffolding that is needed to convey your message to others [footnote 2] and share with the world. That is research.

[1] Many find it embarrassing, awkward and out-of-place to write ".... by Cauchy-Schwarz inequality. (This way of applying Cauchy-Schwarz inequality I learned from [ref] which is completely unrelated to the current topic). Next we can bound (5) by..."

[2] After spending much time thinking about X, you will find that you need to spend much time to explain the basics of X to anyone who has not spent the same time thinking about X. That is why you need all that scaffolding.

What you describe (look at paper, understand it in minute detail, look at next paper) is a depth-first search. This is probably a bad idea (oblig. xkcd).

It's very common at the beginning of a PhD to do a proper literature study. This means writing a report (maybe just for yourself and your supervisor) that summarises everything the human race knows about convex optimisation. Of course, this will not include detailed proofs of everything. The point is to get an overview of the field. If you're lucky, someone has recently written a review paper in your (sub)field, which helps a lot.

When you have an overview, you will (hopefully) at least know one very important thing: which problems have been solved, and which problems are still unsolved, or solved in a poor way? Then comes the hard work: trying to come closer to solving the unsolved problems in your chosen sub-sub-field.