| Summary: | One of the simplest optimization methods for solving unconstrained optimization
problems is the steepest descent (SD) method. The main ad antage of the SD algorithm
with exact line search is that it satisfies global convergence properties under suitable
assumptions. This method requires only the first derivative to be solved for the search
direction which leads to low computational cost and storage requirements. However,
the method has a slow convergence rate based on the higher number of iterations and
central processing unit (CPU) time. Therefore, a new SD method that possesses lower
iterations and CPU time is needed. This research concerns on the development of the
SD method for solving large-scale nonlinear unconstrained optimization problems by
suggesting new search direction in SD algorithm. This study focuses on the
modification f search direction for SD methods by adding new parameters to the
clas ical SD direction with the first suggestion is in two-term direction. Secondly, this
work has also developed a three-term search direction for the SD method with two
different parameters. The proposed method is specifically designed for solving large
scale optimization problems under exact line search procedures. A new formulation of
search direction for SD method combined with the conjugate gradient coefficients has
been suggested. Twenty-six test problems are tested under different initial points
ranging from two to five thousand variables. Numerical results for all of these methods
are compared with existing SD methods based on the number of iterations and CPU
time in which each method is evaluated over the same set of test problems and are
interpreted by using the performance profile. The applicability of the introduced
methods is shown by applying in least square method to solve some chosen nonlinear
ordinary differential equations and to be implemented on data fitting through regression
analysis. A set of data regarding relationship between fin length and total length of silky
shark species has been chosen to construct a linear regression model. Theoretical proofs
showed that all fthe proposed search directions fulfil sufficient descent conditions and
the global c nvergence properties. Numerical results using performance profile indicate
that all of the e methods give superior performance compared to the Classical SD
(SDC), Zubai'ah, Mustafa, Rivaie and Ismail (ZMRI) and Rashidah, Rivaie, Mustafa
(RRM) methods as they are able to lessen the nu : of iterations and CPU time.
Results also show that all of these new methods are applicable 11 aily life problem and
could produce useful regression equations. In conclusion, the numerical results for all
the proposed methods are able to minimize the number of iterations and CPU time.
Besides, the methods also have capabilities to be implemented in the least squar
method and regression analysis for solving the nonlinear ordinary differential equations
and real-life problems.
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