1 / 10

Questions

Questions. What is “f”? What is “x”? How large is “n”? What is the relation between “f” and “x”?. Convexity. Positive Definite. Iterative Algorithms. Starting at x 0 , generate a sequence of iterates { x k } and terminate when no more progress can be made or solution is obtained.

rowdy
Télécharger la présentation

Questions

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Questions • What is “f”? • What is “x”? • How large is “n”? • What is the relation between “f” and “x”?

  2. Convexity

  3. Positive Definite

  4. Iterative Algorithms • Starting at x0, generate a sequence of iterates {xk} and terminate when no more progress can be made or solution is obtained. • From one iterate xk to the next iterate xk+1, the value of the objective must decrease. • To generate the next iterate xk+1, we need information from the current and previous iterates.

  5. Two Types of Algorithms • Line Search (two-steps) • Find a direction to move into • Find an optimal length to travel • Trust Region • Construct a “model function” that approximates the objective function at the current iterate within a “trust region”. • Find the minimizer of the model function. • If the minimizer does not produce enough reduction in the objective function, reduce the approximation region.

  6. Search Directions in Line Search Algorithms– negative gradient

  7. Search Directions in Line Search Algorithms—Newton Step

  8. Search Directions in Line Search Algorithms—Quasi-Newton Step

  9. Search Directions in Line Search Algorithms—Conjugate-gradient Step

More Related