| Summary: | Conjugate Gradiet (CG) methods one of the most popular methods for solving
unconstrained optimization problems due to its simplicity and ability to improve low
memory requirement and computational cost. However, the CG method has a weak
global convergence, low-performance in terms of number of iterations and the Central
Processing Unit (CPU) time. To overcome these problems, a procedure under exact and
inexact line search techniques is introduced. Hybrid CG methods of Polak-Ribiere
Polyak, Wei-Yao-Liu (PRP-WYL) and Polak-Ribiere-Polyak, Dai-Wen (PRP
DWPRP) under some mild condition are suggested. PRP-WYL and PRP-DWPRP are
combined together using exact, inexact line search methods and satisfies the sufficient
descent and global convergence properties correspondence with the PRP ~ WYL ~md
DWPRP CG methods to form a hybrid CG method. On the th r hand, the condition
imposed on exact line search method resolves to be zero while for inexact line search
method the condition would be less than or equal to the square of norm of the gradient
function. The importance of these approaches is to reduce the CPU time and number of
iterations respectively. Complete computational experiments are carried out to compare
PRP-WYL and PRP-DWPRP with other CG methods for solving unconstrained
optimization problems based on number of iterations and CPU time. All the methods
are tested on one hundred and thirty-seven standard optimization test functions using
MATLAB version R2014a subroutine program on 2.40Gz CPU processor, with 4GB
RAM memory and Windows XP professional operating system. For each standard !est
functions, four initial values are selected using dimensions ranging from two to ten
thousand variables. The numerical results are analysed using the performance profile.
The numerical results showed that the proposed Hybrid CG methods performed
remarkably and effectively on some CG methods in terms of CPU time and number of
iterations. The Hybrid CG methods could solve the entire standard test functions with
100% of success compared to Polak-Ribiere-Polyak (PRP) method with 93%, Fletcher
Reeves (FR) with 72%, Dai-Wen (DWPRP) method with 88.4% and Wei-Yao-Liu
(WYL) method with 98%. Hybrid CG methods are effective, efficient and reliable in
terms of number of iterations and CPU time. Furthermore, the proposed methods
possess a global convergence as well as sufficient descent properties and can be an
alternative to the CG methods for solving large scale unconstrained optimization
problems.
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