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The Comparison between Different Versions of
Conjugate Gradient in Minimization Problems
Yan Lai Lee
Supervisor: Dr. Nur Fadhilah Binti Ibrahim
Bachelor of Science (Financial Mathematics)
School of Informatics and Applied Mathematics
Optimization is widely used in many fields such as mathematics, economics and
engineering. One of the useful mathematical technique is the conjugate gradient method.
However, different conjugate gradient methods correspond to different versions of the
parameter β k . The different versions of the parameter have different rate of convergence.
Besides that, the Polak-Ribiere-Polyak (PRP) method is generally regarded to be one of
the most efficient conjugate gradient methods. This research aims to compare the three
different modified PRP method which are β k BZAU , β k SRMI , β k
MRM
with exact line search in
minimization problem, to determine which version is the most efficient conjugate gradient
version as well as to identify the similarities and differences between the versions of the
parameter β k . In this research, the algorithm of conjugate gradient is used to solve
optimization problems and compared by changing the parameter β k which are β k BZAU ,
β k SRMI , β k MRM . The number of iterations and Central Processing Unit (CPU) time per second
for each of the β k will be computed by the MATLAB. The results showed that β k
BZAU
is
the most efficient version of modified PRP Moreover, the similarities and difference
between the versions of the parameter β k were identified after comparing both methods.
906 | UMT UNDERGRADUATE RESEARCH DAY 2018