Looking for book or lecture note recommendations on numerical optimization that (ideally) have the following:
- Emphasis on geometric and physical intuition
- Emphasis on symplectic integrators
- Many well-thought out figures
- Relatively self-contained (some of my background below)
I don't have what's called a "use case", but one of my goals is to able to better-understand i) how to code a symplectic integrator and ii) some intuition as to what math may be useful to advance the recent paper by M. Jordan et al.'s On Symplectic Optimization.
Background: pure mathematics (algebraic geometry) and some background in physics. Never studied Hamiltonian dynamics proper and don't know what a "geometric integrator" is beyond the lovely Wikipedia article on it. Also used some of the standard gradient descent methods such as Nesterov and Adam in practice (ML), but can't say I really know the "physics" behind these methods.
I haven't checked out the books by Hairer et al or Leimkuhler -- would one (or both?) fit the bill? It would be very useful to get comments on these books.