SESG6018 (Design Search and Optimisation) Exam 2008/09
Answer all of the following four short questions (total time
allowed 1 hour) and then one of the long essay questions (total
time allowed 1 hour).
Short Questions – answer all four questions.
S1) The function f ( x)  x5  2 x3 10 x  5 is to be minimized using
Newton’s method starting from x  1 . Carry out two iterations of
the scheme, clearly showing how you have derived each new
iterate.
S2) The function f ( x)  x5  2 x3 10 x  5 is to be minimized using
inverse parabolic interpolation starting from evaluations at
x  0,1,2 . Carry out two iterations of the scheme, clearly showing
how you have derived each new iterate.
S3) A least squares parabolic curve fit to four data points may be
obtained using SVD. If the data points are given at x  1,0,1,2
write down the matrix equation relating the function values of
y  1,0,1,2 at these x values and the coefficients of the fitting
parabola a, b and c. What then are the values of a, b and c for the
parabolic curve fit given these data? Derive an estimate of the
function value at x  0.5 .
1  1 1



0
0 1 
'
You may assume that if the SVD of 
 isU .w.V then it
1 1 
1


2 1 
4
may be shown that
 0.25
 0.25  0.25 0.25 




0
.
55
0
.
15
0
.
35
0
.
05

V .diag(1/ w j ).U '  
.
0.55
0.45  0.15
 0.15




S4) The function f ( x1, x2 )  x1  x2  2x1 x2 2  x23 is to be minimized
using the Hooke and Jeeves method, starting from the point (0,1)
with an initial step size of +0.1. Carry out two iterations of the
scheme, clearly showing how you have decided the correct
pattern moves and whether these have been accepted and thus
how you have derived the new iterates.
Long questions – answer only one of the three questions, only
the first answer on your script will be marked.
L1) Describe the role of parameterization in design and design
optimization & search, paying attention to flexibility, robustness,
ease of use and development costs.
L2) Describe the steps involved in using a surrogate model to
support a design optimization process, paying particular attention
to experiment and surrogate design, validation and updating.
L3) Describe the way the optimization tools may used to tackle
design problems with multiple goals, paying particular attention
to how goals may be combined or dealt with simultaneously.