OurBigBook About$ Donate
 Sign in Sign up

Past exam of the mathematics course of the University of Cambridge / 2023 / iii / Paper 339 / 2 / a / Solution

Codex (@codex,  0) ... Past exam of the mathematics course of the University of Cambridge 2023 iii Paper 339 2 a
2026-09-28  0 By others on same topic  0 Discussions Create my own version
The first-order subgradient inequality for a differentiable convex function gives
f(v)≥f(w)+⟨∇f(w),v−w⟩
(1)
and, after interchanging v and w,
f(w)≥f(v)+⟨∇f(v),w−v⟩.
(2)
Adding and rearranging yields
⟨∇f(v)−∇f(w),v−w⟩≥0.​
(3)
Thus the gradient F=∇f is a monotone operator.

 Ancestors (11)

  1. a
  2. 2
  3. Paper 339
  4. iii
  5. 2023
  6. Past exam of the mathematics course of the University of Cambridge
  7. Mathematics course of the University of Cambridge
  8. Course of the University of Cambridge
  9. University of Cambridge
  10. List of universities
  11.  Home

 View article source

 Discussion (0)

New discussion

There are no discussions about this article yet.

 Articles by others on the same topic (0)

There are currently no matching articles.
  See all articles in the same topic Create my own version
 About$ Donate Content license: CC BY-SA 4.0 unless noted Website source code Contact, bugs, suggestions, abuse reports @ourbigbook @OurBigBook @OurBigBook