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Paper details
Number 2 - June 2024
Volume 34 - 2024
A descent generalized RMIL spectral gradient algorithm for optimization problems
Ibrahim M. Sulaiman, P. Kaelo, Ruzelan Khalid, Mohd Kamal M. Nawawi
Abstract
This study develops a new conjugate gradient (CG) search direction that incorporates a well defined spectral parameter while
the step size is required to satisfy the famous strong Wolfe line search (SWP) strategy. The proposed spectral direction is
derived based on a recent method available in the literature, and satisfies the sufficient descent condition irrespective of the
line search strategy and without imposing any restrictions or conditions. The global convergence results of the new formula
are established using the assumption that the gradient of the defined smooth function is Lipschitz continuous. To illustrate
the computational efficiency of the new direction, the study presents two sets of experiments on a number of benchmark
functions. The first experiment is performed by setting uniform SWP parameter values for all the algorithms considered
for comparison. For the second experiment, the study evaluates the performance of all the algorithms by considering the
exact SWP parameter values used for the numerical experiments as reported in each work. The idea of these experiments
is to study the influence of parameters in the computational efficiency of various CG algorithms. The results obtained
demonstrate the effect of the parameter value on the robustness of the algorithms.
Keywords
optimization models, spectral CG algorithm, global convergence, line search strategy