Numerical Optimization: Difference between revisions
Created page with "Numerical Optimization ==Line Search Methods== Basic idea: * For each iteration< ** Find a direction <math>p</math>. ** Then find a step length <math>\alpha</math> which d..." |
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Basic idea: | Basic idea: | ||
* For each iteration | * For each iteration | ||
** Find a direction <math>p</math>. | ** Find a direction <math>p</math>. | ||
** Then find a step length <math>\alpha</math> which decreases <math>f</math>. | ** Then find a step length <math>\alpha</math> which decreases <math>f</math>. | ||
Revision as of 19:44, 31 October 2019
Numerical Optimization
Line Search Methods
Basic idea:
- For each iteration
- Find a direction \(\displaystyle p\).
- Then find a step length \(\displaystyle \alpha\) which decreases \(\displaystyle f\).
- Take a step \(\displaystyle \alpha p\).
Trust Region Methods
Basic idea:
- For each iteration
- Assume a quadratic model of your objective function near a point.
- Find a region where you trust your model accurately represents your objective function.
- Take a step.
Resources
- [https://link.springer.com/book/10.1007%2F978-0-387-40065-5 Numerical Optimization by Nocedal and Wright (2006)