About the maths formula for optimization

Hello. I admire your paper very much,especially the part of math.

And during my reading, I meet a confusion about the process for optimization.

It 's about quadratic approximation from Formula 11 to Formula 12 in Part B. I think the Formula 11 is about  taylor expansion or gradient Lipschitz. But I have no idea how to deduce Formula 12.

Could you give a clear explanation?

Thank you.
