NM6_optim_s02 - CGN 3421 - Computer Methods Gurley...

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon
CGN 3421 - Computer Methods Gurley Numerical Methods Lecture 6 - Optimization page 103 of 111 Numerical Methods Lecture 6 - Optimization NOTE: The unit on differential equations will not be available online. We will use notes on the board only. Topics: numerical optimization - Newton again - Random search - Golden Section Search Optimization - motivation What? Locating where some function reaches a maximum or minimum Find x where or Why? For example: A function represents the cost of a project minimize the cost of the project When? When an exact solution is not available or a big pain Example 1: Given: , Find x where y is minimum analytical solution: ==> Example 2: Given: , Find x where y is minimum Depends on the range we’re interested in. .. Having lots of local maxima and minima means having lots of zero slope cases. An exact solution would be a big pain. .. ! " () #$" ! !" #%& ! "# " $ % & ! (’ (" ----- (& " $ % ) !! " $ ! ’" *+, $ (-" " " % *+, % ./0 !
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
CGN 3421 - Computer Methods Gurley Numerical Methods Lecture 6 - Optimization page 104 of 111 Single variable - Newton Recall the Newton method for finding a root of an equation , where We can use a similar approach to find a min or max of The min / max occurs where the slope is zero So if we find the root of the derivative, we find the max / min location Find roots of using Newton = Example: Newton Method find the maximum of this function we’ll need these for x = [0,3] OR we can use central difference to replace the analytical derivatives. " ) ( " ) !" ) () ! 2 " ) ---------------- % ! ! 2 " ) (! " (" ------------ ! ! " ! 2 " *" ) !! " ) ( " ) ) * ' " ) -------------- % ! " ) ! 2 " ! 22 " --------------- % to find where the max occurs. .. find the root of the function’s derivative ! " " 3 " " $ & " & %& 3 " % !
Background image of page 2
Image of page 3
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 05/18/2011 for the course CGN 3421 taught by Professor Long during the Spring '08 term at University of Florida.

Page1 / 9

NM6_optim_s02 - CGN 3421 - Computer Methods Gurley...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online