Molecular Modeling Assignment

 

 

For these exercises you can use the Java Applets found at (http://www.cse.uiuc.edu/eot/modules/optimization)

  1.  

Find the all the minima of the following functions using the parabolic method and NewtonÕs method.

Record the # of iterations required to reach the extrema. Compare the two methods.

 

    1. F(x)=x2-3x+5
    2. F(x)=x4-3x3+x-3.14

 

  1. Using any two of the two-dimensional methods listed find the minimum of the following function starting at a point a) close to a minimum b) a point far from a minimum:

 

F(x,y) = -.5x2+.25x4+.25y4

 

                                                     i.     Record the # of iterations for each

                                                      ii.     Compare the two methods.  Which is best?

 

   Repeat for the function: 

 

F(x,y)=-.5x2+.25x4+.25xy2+.1y4

 

Is the minimum a global minimum?