7
$\begingroup$

Explicit Request

Looking for book or lecture note recommendations on numerical optimization that (ideally) have the following:

  1. Emphasis on geometric and physical intuition
  2. Emphasis on symplectic integrators
  3. Many well-thought out figures
  4. Relatively self-contained (some of my background below)
  5. Pseudo-code

Goals

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.

Thank you!

Addenda

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.

$\endgroup$
  • 3
    $\begingroup$ Have you taken a look at Hairer et al.'s Geometric Numerical Integration? $\endgroup$ – Rodrigo de Azevedo Jun 20 '18 at 6:44
  • $\begingroup$ Only the amazon.com entry and the three customer reviews therein. I wasn't able to find an electronic copy and didn't want to shell out $90 USD immediately. Does that book fit the five points above? $\endgroup$ – Quetzalcoatl Jun 20 '18 at 6:46
  • 1
    $\begingroup$ I second the recommendation for Hairer et al. I think the book satisfies all your requirements except point 5, but given your background I don't think that will be too much of a problem. $\endgroup$ – Rahul Jun 20 '18 at 7:12
  • 1
    $\begingroup$ You also might want to take a look at McLachlan-Quispel survey and their lectures. $\endgroup$ – Evgeny Jun 20 '18 at 16:54
  • 2
    $\begingroup$ Another resource that may be of interest with regards to the symplectic integration side of things is this scicomp.stackexchange post: scicomp.stackexchange.com/questions/29149/… $\endgroup$ – Kyle Jun 21 '18 at 18:54

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Browse other questions tagged or ask your own question.