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NM6_optim_s02

# NM6_optim_s02 - CGN 3421 Computer Methods Gurley Numerical...

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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 !

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