| Summary: | Conjugate gradient methods are a family of significance methods for solving of
large-scale unconstrained optimization problems. This is due to both the simplicity
of its algorithm and low memory requirement. A lot of efforts have been done to
improve those methods since 1964 when the work of Fletcher and Reeve had opened
the way to nonlinear conjugate gradient methods. In this research two new simple
modifications of conjugate gradient coefficient 13k have been proposed. Both
algorithms satisfy sufficient descent conditions and global convergence for exact line
search and strong Wolfe line search. The convergence rate is super linear and its
search directions fulfill the angle conditions. Based on the fact that a proof of global
convergence for an algorithm does not ensure that it is an efficient method, then the
new 13k is tested with twenty eight standard optimization test problems using
MATLAB version 7.10.0 (R 2010a) subroutine programming and compared with
five well- known conjugate gradient methods, which are Fletcher and Reeves (FR),
Polak-Ribiere-Polyak (PRP), Hestenes and Steifel (HS), Wei-Yao-Liu (WYL) and
Dai and Yuan (DY). Numerical results based on number of iterations and CPU time
are analyzed and presented using performance profile of Dolan and Moore. For
every test function four initial points are selected, some are close to the solution and
some are further away. It is found out that both new formulas perform better than the
other formulas for exact line search. However IMRI performs better than the other
formulas for strong Wolfe line search.
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