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Write a MATLAB program to find the minimum of the function fcd ( ) where cd = 1 8 from [ 2 , Appendix B
Write a MATLAB program to find the minimum of the function fcd where cd from
Appendix B by using
NewtonRaphson,
HestenesStiefel,
PolakRibiere and
FletcherReeves algorithms.
You are also strongly encouraged to use another relevant algorithm from the literature, which will
be rewarded with an extra points. If the function is not differentiable, use an approximation
proposed by yourself or an relevant approximation commonly used in the literature and write it
explicitly in your report. Repeat the main steps of your algorithms until the desired accuracy is
achieved, ie
fxk and fxk fxk
Take THREE initial guess as x Nnndimensional vector having elements from standard
normal distribution by using randn function of MATLAB or x Unxmin, xmaxndimensional
vector having elements from uniform distribution from the closed interval xmin, xmax where
xmin and xmax are specified for each function in by using rand function of MATLAB For
instance, if your problem is defined on xi for i you may consider to choose
x Un Take also the absolute error bound as
for every algorithm.
Instructions
Write a project report regarding to the given task by answering the following questions please
EXPLAIN all of them by at least two sentences:
p How many steps does it take to find the minimum of this function with all of these
algorithms?
p What are the execution times of these algorithms? Does this make sense?
p Does the convergence depend on the initial conditions? Why?
p Based on the last two questions, what can be the reason for this tradeoff?
p Do you expect the same number of steps and execution times, when you change the
stopping criterion and the absolute error bound?
Your project report also MUST
p contain at least one figure if your problem is dimensional, then your figure must include
the all the steps starting from THREE random initial points with DIFFERENT COLORS
and all the steps corresponding to the same iteration MUST be plotted with the SAME
COLOR!
p contain at least one table for benchmark,
p be at least two pages long and be written by IEEE conference proceeding template
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